// ---------------------------------------------------------------------------
// Copyright (c) 2019, Gregory Popovitch - greg7mdp@gmail.com
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Includes work from abseil-cpp (https://github.com/abseil/abseil-cpp)
// with modifications.
//
// Copyright 2018 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ---------------------------------------------------------------------------

#ifndef PHMAP_BTREE_BTREE_CONTAINER_H_
#define PHMAP_BTREE_BTREE_CONTAINER_H_

#ifdef _MSC_VER
#pragma warning(push)

#pragma warning(disable : 4127) // conditional expression is constant
#pragma warning(disable : 4324) // structure was padded due to alignment specifier
#pragma warning(disable : 4355) // 'this': used in base member initializer list
#pragma warning(disable : 4365) // conversion from 'int' to 'const unsigned __int64', signed/unsigned mismatch
#pragma warning(disable : 4514) // unreferenced inline function has been removed
#pragma warning(disable : 4623) // default constructor was implicitly defined as deleted
#pragma warning(disable : 4625) // copy constructor was implicitly defined as deleted
#pragma warning(disable : 4626) // assignment operator was implicitly defined as deleted
#pragma warning(disable : 4710) // function not inlined
#pragma warning(disable : 4711) //  selected for automatic inline expansion
#pragma warning(disable : 4820) // '6' bytes padding added after data member
#pragma warning(disable : 4868) // compiler may not enforce left-to-right evaluation order in braced initializer list
#pragma warning(disable : 5026) // move constructor was implicitly defined as deleted
#pragma warning(disable : 5027) // move assignment operator was implicitly defined as deleted
#pragma warning(disable : 5045) // Compiler will insert Spectre mitigation for memory load if /Qspectre switch specified
#endif


#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <limits>
#include <new>
#include <type_traits>

#include "phmap_fwd_decl.h"
#include "phmap_base.h"

#if PHMAP_HAVE_STD_STRING_VIEW
#include <string_view>
#endif

// MSVC constructibility traits do not detect destructor properties and so our
// implementations should not use them as a source-of-truth.
#if defined(_MSC_VER) && !defined(__clang__) && !defined(__GNUC__)
#define PHMAP_META_INTERNAL_STD_CONSTRUCTION_TRAITS_DONT_CHECK_DESTRUCTION 1
#endif

namespace phmap {

	namespace type_traits_internal {

// Silence MSVC warnings about the destructor being defined as deleted.
#if defined(_MSC_VER) && !defined(__GNUC__)
#pragma warning(push)
#pragma warning(disable : 4624)
#endif  // defined(_MSC_VER) && !defined(__GNUC__)

		template <class T>
		union SingleMemberUnion {
			T t;
		};

// Restore the state of the destructor warning that was silenced above.
#if defined(_MSC_VER) && !defined(__GNUC__)
#pragma warning(pop)
#endif  // defined(_MSC_VER) && !defined(__GNUC__)

		template <class T>
		struct IsTriviallyMoveConstructibleObject
			: std::integral_constant<
			  bool, std::is_move_constructible<
			  type_traits_internal::SingleMemberUnion<T>>::value &&
			  std::is_trivially_destructible<T>::value> {};

		template <class T>
		struct IsTriviallyCopyConstructibleObject
			: std::integral_constant<
			  bool, std::is_copy_constructible<
			  type_traits_internal::SingleMemberUnion<T>>::value &&
			  std::is_trivially_destructible<T>::value> {};

		template <class T>
		struct IsTriviallyMoveAssignableReference : std::false_type {};

		template <class T>
		struct IsTriviallyMoveAssignableReference<T&>
			: std::is_trivially_move_assignable<T>::type {};

		template <class T>
		struct IsTriviallyMoveAssignableReference<T&&>
			: std::is_trivially_move_assignable<T>::type {};

	}  // namespace type_traits_internal


	template <typename... Ts>
	using void_t = typename type_traits_internal::VoidTImpl<Ts...>::type;


	template <typename T>
	struct is_function
		: std::integral_constant<
	  bool, !(std::is_reference<T>::value ||
	          std::is_const<typename std::add_const<T>::type>::value)> {};


	namespace type_traits_internal {

		template <typename T>
		class is_trivially_copyable_impl {
			using ExtentsRemoved = typename std::remove_all_extents<T>::type;
			static constexpr bool kIsCopyOrMoveConstructible =
			    std::is_copy_constructible<ExtentsRemoved>::value ||
			    std::is_move_constructible<ExtentsRemoved>::value;
			static constexpr bool kIsCopyOrMoveAssignable =
			    phmap::is_copy_assignable<ExtentsRemoved>::value ||
			    phmap::is_move_assignable<ExtentsRemoved>::value;

		public:
			static constexpr bool kValue =
			    (std::is_trivially_copyable<ExtentsRemoved>::value || !kIsCopyOrMoveConstructible) &&
			    (std::is_trivially_copy_assignable<ExtentsRemoved>::value || !kIsCopyOrMoveAssignable) &&
			    (kIsCopyOrMoveConstructible || kIsCopyOrMoveAssignable) &&
			    std::is_trivially_destructible<ExtentsRemoved>::value &&
			    // We need to check for this explicitly because otherwise we'll say
			    // references are trivial copyable when compiled by MSVC.
			    !std::is_reference<ExtentsRemoved>::value;
		};

		template <typename T>
		struct is_trivially_copyable
			: std::integral_constant<
			  bool, type_traits_internal::is_trivially_copyable_impl<T>::kValue> {};
	}  // namespace type_traits_internal

	namespace swap_internal {

// Necessary for the traits.
		using std::swap;

// This declaration prevents global `swap` and `phmap::swap` overloads from being
// considered unless ADL picks them up.
		void swap();

		template <class T>
		using IsSwappableImpl = decltype(swap(std::declval<T&>(), std::declval<T&>()));

// NOTE: This dance with the default template parameter is for MSVC.
		template <class T,
		          class IsNoexcept = std::integral_constant<
		              bool, noexcept(swap(std::declval<T&>(), std::declval<T&>()))>>
		using IsNothrowSwappableImpl = typename std::enable_if<IsNoexcept::value>::type;

		template <class T>
		struct IsSwappable
			: phmap::type_traits_internal::is_detected<IsSwappableImpl, T> {};

		template <class T>
		struct IsNothrowSwappable
			: phmap::type_traits_internal::is_detected<IsNothrowSwappableImpl, T> {};

		template <class T, phmap::enable_if_t<IsSwappable<T>::value, int> = 0>
		void Swap(T& lhs, T& rhs) noexcept(IsNothrowSwappable<T>::value)
		{
			swap(lhs, rhs);
		}

		using StdSwapIsUnconstrained = IsSwappable<void()>;

	}  // namespace swap_internal

	namespace type_traits_internal {

// Make the swap-related traits/function accessible from this namespace.
		using swap_internal::IsNothrowSwappable;
		using swap_internal::IsSwappable;
		using swap_internal::Swap;
		using swap_internal::StdSwapIsUnconstrained;

	}  // namespace type_traits_internal

	namespace compare_internal {

		using value_type = int8_t;

		template <typename T>
		struct Fail {
			static_assert(sizeof(T) < 0, "Only literal `0` is allowed.");
		};

		template <typename NullPtrT = std::nullptr_t>
		struct OnlyLiteralZero {
			constexpr OnlyLiteralZero(NullPtrT) noexcept {}  // NOLINT

			template <
			    typename T,
			    typename = typename std::enable_if<
			        std::is_same<T, std::nullptr_t>::value ||
			        (std::is_integral<T>::value && !std::is_same<T, int>::value)>::type,
			    typename = typename Fail<T>::type>
			OnlyLiteralZero(T);  // NOLINT
		};

		enum class eq : value_type {
			equal = 0,
			equivalent = equal,
			nonequal = 1,
			nonequivalent = nonequal,
		};

		enum class ord : value_type { less = -1, greater = 1 };

		enum class ncmp : value_type { unordered = -127 };

#if defined(__cpp_inline_variables) && !defined(_MSC_VER)

#define PHMAP_COMPARE_INLINE_BASECLASS_DECL(name)

#define PHMAP_COMPARE_INLINE_SUBCLASS_DECL(type, name)  \
        static const type name;

#define PHMAP_COMPARE_INLINE_INIT(type, name, init) \
        inline constexpr type type::name(init)

#else  // __cpp_inline_variables

#define PHMAP_COMPARE_INLINE_BASECLASS_DECL(name)   \
        static const T name;

#define PHMAP_COMPARE_INLINE_SUBCLASS_DECL(type, name)

#define PHMAP_COMPARE_INLINE_INIT(type, name, init)             \
        template <typename T>                                   \
        const T compare_internal::type##_base<T>::name(init)

#endif  // __cpp_inline_variables

// These template base classes allow for defining the values of the constants
// in the header file (for performance) without using inline variables (which
// aren't available in C++11).
		template <typename T>
		struct weak_equality_base {
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(equivalent)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(nonequivalent)
		};

		template <typename T>
		struct strong_equality_base {
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(equal)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(nonequal)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(equivalent)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(nonequivalent)
		};

		template <typename T>
		struct partial_ordering_base {
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(less)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(equivalent)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(greater)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(unordered)
		};

		template <typename T>
		struct weak_ordering_base {
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(less)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(equivalent)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(greater)
		};

		template <typename T>
		struct strong_ordering_base {
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(less)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(equal)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(equivalent)
			PHMAP_COMPARE_INLINE_BASECLASS_DECL(greater)
		};

	}  // namespace compare_internal

	class weak_equality
		: public compare_internal::weak_equality_base<weak_equality> {
		explicit constexpr weak_equality(compare_internal::eq v) noexcept
			: value_(static_cast<compare_internal::value_type>(v)) {}
		friend struct compare_internal::weak_equality_base<weak_equality>;

	public:
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(weak_equality, equivalent)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(weak_equality, nonequivalent)

		// Comparisons
		friend constexpr bool operator==(
		    weak_equality v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ == 0;
		}
		friend constexpr bool operator!=(
		    weak_equality v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ != 0;
		}
		friend constexpr bool operator==(compare_internal::OnlyLiteralZero<>,
		                                 weak_equality v) noexcept
		{
			return 0 == v.value_;
		}
		friend constexpr bool operator!=(compare_internal::OnlyLiteralZero<>,
		                                 weak_equality v) noexcept
		{
			return 0 != v.value_;
		}

	private:
		compare_internal::value_type value_;
	};
	PHMAP_COMPARE_INLINE_INIT(weak_equality, equivalent,
	                          compare_internal::eq::equivalent);
	PHMAP_COMPARE_INLINE_INIT(weak_equality, nonequivalent,
	                          compare_internal::eq::nonequivalent);

	class strong_equality
		: public compare_internal::strong_equality_base<strong_equality> {
		explicit constexpr strong_equality(compare_internal::eq v) noexcept
			: value_(static_cast<compare_internal::value_type>(v)) {}
		friend struct compare_internal::strong_equality_base<strong_equality>;

	public:
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(strong_equality, equal)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(strong_equality, nonequal)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(strong_equality, equivalent)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(strong_equality, nonequivalent)

		// Conversion
		constexpr operator weak_equality() const noexcept    // NOLINT
		{
			return value_ == 0 ? weak_equality::equivalent
			       : weak_equality::nonequivalent;
		}
		// Comparisons
		friend constexpr bool operator==(
		    strong_equality v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ == 0;
		}
		friend constexpr bool operator!=(
		    strong_equality v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ != 0;
		}
		friend constexpr bool operator==(compare_internal::OnlyLiteralZero<>,
		                                 strong_equality v) noexcept
		{
			return 0 == v.value_;
		}
		friend constexpr bool operator!=(compare_internal::OnlyLiteralZero<>,
		                                 strong_equality v) noexcept
		{
			return 0 != v.value_;
		}

	private:
		compare_internal::value_type value_;
	};

	PHMAP_COMPARE_INLINE_INIT(strong_equality, equal, compare_internal::eq::equal);
	PHMAP_COMPARE_INLINE_INIT(strong_equality, nonequal,
	                          compare_internal::eq::nonequal);
	PHMAP_COMPARE_INLINE_INIT(strong_equality, equivalent,
	                          compare_internal::eq::equivalent);
	PHMAP_COMPARE_INLINE_INIT(strong_equality, nonequivalent,
	                          compare_internal::eq::nonequivalent);

	class partial_ordering
		: public compare_internal::partial_ordering_base<partial_ordering> {
		explicit constexpr partial_ordering(compare_internal::eq v) noexcept
			: value_(static_cast<compare_internal::value_type>(v)) {}
		explicit constexpr partial_ordering(compare_internal::ord v) noexcept
			: value_(static_cast<compare_internal::value_type>(v)) {}
		explicit constexpr partial_ordering(compare_internal::ncmp v) noexcept
			: value_(static_cast<compare_internal::value_type>(v)) {}
		friend struct compare_internal::partial_ordering_base<partial_ordering>;

		constexpr bool is_ordered() const noexcept
		{
			return value_ !=
			       compare_internal::value_type(compare_internal::ncmp::unordered);
		}

	public:
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(partial_ordering, less)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(partial_ordering, equivalent)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(partial_ordering, greater)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(partial_ordering, unordered)

		// Conversion
		constexpr operator weak_equality() const noexcept    // NOLINT
		{
			return value_ == 0 ? weak_equality::equivalent
			       : weak_equality::nonequivalent;
		}
		// Comparisons
		friend constexpr bool operator==(
		    partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.is_ordered() && v.value_ == 0;
		}
		friend constexpr bool operator!=(
		    partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return !v.is_ordered() || v.value_ != 0;
		}
		friend constexpr bool operator<(
		    partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.is_ordered() && v.value_ < 0;
		}
		friend constexpr bool operator<=(
		    partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.is_ordered() && v.value_ <= 0;
		}
		friend constexpr bool operator>(
		    partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.is_ordered() && v.value_ > 0;
		}
		friend constexpr bool operator>=(
		    partial_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.is_ordered() && v.value_ >= 0;
		}
		friend constexpr bool operator==(compare_internal::OnlyLiteralZero<>,
		                                 partial_ordering v) noexcept
		{
			return v.is_ordered() && 0 == v.value_;
		}
		friend constexpr bool operator!=(compare_internal::OnlyLiteralZero<>,
		                                 partial_ordering v) noexcept
		{
			return !v.is_ordered() || 0 != v.value_;
		}
		friend constexpr bool operator<(compare_internal::OnlyLiteralZero<>,
		                                partial_ordering v) noexcept
		{
			return v.is_ordered() && 0 < v.value_;
		}
		friend constexpr bool operator<=(compare_internal::OnlyLiteralZero<>,
		                                 partial_ordering v) noexcept
		{
			return v.is_ordered() && 0 <= v.value_;
		}
		friend constexpr bool operator>(compare_internal::OnlyLiteralZero<>,
		                                partial_ordering v) noexcept
		{
			return v.is_ordered() && 0 > v.value_;
		}
		friend constexpr bool operator>=(compare_internal::OnlyLiteralZero<>,
		                                 partial_ordering v) noexcept
		{
			return v.is_ordered() && 0 >= v.value_;
		}

	private:
		compare_internal::value_type value_;
	};

	PHMAP_COMPARE_INLINE_INIT(partial_ordering, less, compare_internal::ord::less);
	PHMAP_COMPARE_INLINE_INIT(partial_ordering, equivalent,
	                          compare_internal::eq::equivalent);
	PHMAP_COMPARE_INLINE_INIT(partial_ordering, greater,
	                          compare_internal::ord::greater);
	PHMAP_COMPARE_INLINE_INIT(partial_ordering, unordered,
	                          compare_internal::ncmp::unordered);

	class weak_ordering
		: public compare_internal::weak_ordering_base<weak_ordering> {
		explicit constexpr weak_ordering(compare_internal::eq v) noexcept
			: value_(static_cast<compare_internal::value_type>(v)) {}
		explicit constexpr weak_ordering(compare_internal::ord v) noexcept
			: value_(static_cast<compare_internal::value_type>(v)) {}
		friend struct compare_internal::weak_ordering_base<weak_ordering>;

	public:
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(weak_ordering, less)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(weak_ordering, equivalent)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(weak_ordering, greater)

		// Conversions
		constexpr operator weak_equality() const noexcept    // NOLINT
		{
			return value_ == 0 ? weak_equality::equivalent
			       : weak_equality::nonequivalent;
		}
		constexpr operator partial_ordering() const noexcept    // NOLINT
		{
			return value_ == 0 ? partial_ordering::equivalent
			       : (value_ < 0 ? partial_ordering::less
			          : partial_ordering::greater);
		}
		// Comparisons
		friend constexpr bool operator==(
		    weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ == 0;
		}
		friend constexpr bool operator!=(
		    weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ != 0;
		}
		friend constexpr bool operator<(
		    weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ < 0;
		}
		friend constexpr bool operator<=(
		    weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ <= 0;
		}
		friend constexpr bool operator>(
		    weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ > 0;
		}
		friend constexpr bool operator>=(
		    weak_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ >= 0;
		}
		friend constexpr bool operator==(compare_internal::OnlyLiteralZero<>,
		                                 weak_ordering v) noexcept
		{
			return 0 == v.value_;
		}
		friend constexpr bool operator!=(compare_internal::OnlyLiteralZero<>,
		                                 weak_ordering v) noexcept
		{
			return 0 != v.value_;
		}
		friend constexpr bool operator<(compare_internal::OnlyLiteralZero<>,
		                                weak_ordering v) noexcept
		{
			return 0 < v.value_;
		}
		friend constexpr bool operator<=(compare_internal::OnlyLiteralZero<>,
		                                 weak_ordering v) noexcept
		{
			return 0 <= v.value_;
		}
		friend constexpr bool operator>(compare_internal::OnlyLiteralZero<>,
		                                weak_ordering v) noexcept
		{
			return 0 > v.value_;
		}
		friend constexpr bool operator>=(compare_internal::OnlyLiteralZero<>,
		                                 weak_ordering v) noexcept
		{
			return 0 >= v.value_;
		}

	private:
		compare_internal::value_type value_;
	};

	PHMAP_COMPARE_INLINE_INIT(weak_ordering, less, compare_internal::ord::less);
	PHMAP_COMPARE_INLINE_INIT(weak_ordering, equivalent,
	                          compare_internal::eq::equivalent);
	PHMAP_COMPARE_INLINE_INIT(weak_ordering, greater,
	                          compare_internal::ord::greater);

	class strong_ordering
		: public compare_internal::strong_ordering_base<strong_ordering> {
		explicit constexpr strong_ordering(compare_internal::eq v) noexcept
			: value_(static_cast<compare_internal::value_type>(v)) {}
		explicit constexpr strong_ordering(compare_internal::ord v) noexcept
			: value_(static_cast<compare_internal::value_type>(v)) {}
		friend struct compare_internal::strong_ordering_base<strong_ordering>;

	public:
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(strong_ordering, less)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(strong_ordering, equal)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(strong_ordering, equivalent)
		PHMAP_COMPARE_INLINE_SUBCLASS_DECL(strong_ordering, greater)

		// Conversions
		constexpr operator weak_equality() const noexcept    // NOLINT
		{
			return value_ == 0 ? weak_equality::equivalent
			       : weak_equality::nonequivalent;
		}
		constexpr operator strong_equality() const noexcept    // NOLINT
		{
			return value_ == 0 ? strong_equality::equal : strong_equality::nonequal;
		}
		constexpr operator partial_ordering() const noexcept    // NOLINT
		{
			return value_ == 0 ? partial_ordering::equivalent
			       : (value_ < 0 ? partial_ordering::less
			          : partial_ordering::greater);
		}
		constexpr operator weak_ordering() const noexcept    // NOLINT
		{
			return value_ == 0
			       ? weak_ordering::equivalent
			       : (value_ < 0 ? weak_ordering::less : weak_ordering::greater);
		}
		// Comparisons
		friend constexpr bool operator==(
		    strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ == 0;
		}
		friend constexpr bool operator!=(
		    strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ != 0;
		}
		friend constexpr bool operator<(
		    strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ < 0;
		}
		friend constexpr bool operator<=(
		    strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ <= 0;
		}
		friend constexpr bool operator>(
		    strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ > 0;
		}
		friend constexpr bool operator>=(
		    strong_ordering v, compare_internal::OnlyLiteralZero<>) noexcept
		{
			return v.value_ >= 0;
		}
		friend constexpr bool operator==(compare_internal::OnlyLiteralZero<>,
		                                 strong_ordering v) noexcept
		{
			return 0 == v.value_;
		}
		friend constexpr bool operator!=(compare_internal::OnlyLiteralZero<>,
		                                 strong_ordering v) noexcept
		{
			return 0 != v.value_;
		}
		friend constexpr bool operator<(compare_internal::OnlyLiteralZero<>,
		                                strong_ordering v) noexcept
		{
			return 0 < v.value_;
		}
		friend constexpr bool operator<=(compare_internal::OnlyLiteralZero<>,
		                                 strong_ordering v) noexcept
		{
			return 0 <= v.value_;
		}
		friend constexpr bool operator>(compare_internal::OnlyLiteralZero<>,
		                                strong_ordering v) noexcept
		{
			return 0 > v.value_;
		}
		friend constexpr bool operator>=(compare_internal::OnlyLiteralZero<>,
		                                 strong_ordering v) noexcept
		{
			return 0 >= v.value_;
		}

	private:
		compare_internal::value_type value_;
	};
	PHMAP_COMPARE_INLINE_INIT(strong_ordering, less, compare_internal::ord::less);
	PHMAP_COMPARE_INLINE_INIT(strong_ordering, equal, compare_internal::eq::equal);
	PHMAP_COMPARE_INLINE_INIT(strong_ordering, equivalent,
	                          compare_internal::eq::equivalent);
	PHMAP_COMPARE_INLINE_INIT(strong_ordering, greater,
	                          compare_internal::ord::greater);

#undef PHMAP_COMPARE_INLINE_BASECLASS_DECL
#undef PHMAP_COMPARE_INLINE_SUBCLASS_DECL
#undef PHMAP_COMPARE_INLINE_INIT

	namespace compare_internal {
// We also provide these comparator adapter functions for internal phmap use.

// Helper functions to do a boolean comparison of two keys given a boolean
// or three-way comparator.
// SFINAE prevents implicit conversions to bool (such as from int).
		template <typename BoolType,
		          phmap::enable_if_t<std::is_same<bool, BoolType>::value, int> = 0>
		constexpr bool compare_result_as_less_than(const BoolType r)
		{
			return r;
		}
		constexpr bool compare_result_as_less_than(const phmap::weak_ordering r)
		{
			return r < 0;
		}

		template <typename Compare, typename K, typename LK>
		constexpr bool do_less_than_comparison(const Compare &compare, const K &x,
		                                       const LK &y)
		{
			return compare_result_as_less_than(compare(x, y));
		}

// Helper functions to do a three-way comparison of two keys given a boolean or
// three-way comparator.
// SFINAE prevents implicit conversions to int (such as from bool).
		template <typename Int,
		          phmap::enable_if_t<std::is_same<int, Int>::value, int> = 0>
		constexpr phmap::weak_ordering compare_result_as_ordering(const Int c)
		{
			return c < 0 ? phmap::weak_ordering::less
			       : c == 0 ? phmap::weak_ordering::equivalent
			       : phmap::weak_ordering::greater;
		}
		constexpr phmap::weak_ordering compare_result_as_ordering(
		    const phmap::weak_ordering c)
		{
			return c;
		}

		template <
		    typename Compare, typename K, typename LK,
		    phmap::enable_if_t<!std::is_same<bool, phmap::invoke_result_t<
		            Compare, const K &, const LK &>>::value,
		                       int> = 0>
		constexpr phmap::weak_ordering do_three_way_comparison(const Compare &compare,
		        const K &x, const LK &y)
		{
			return compare_result_as_ordering(compare(x, y));
		}
		template <
		    typename Compare, typename K, typename LK,
		    phmap::enable_if_t<std::is_same<bool, phmap::invoke_result_t<Compare,
		                                    const K &, const LK &>>::value,
		                       int> = 0>
		constexpr phmap::weak_ordering do_three_way_comparison(const Compare &compare,
		        const K &x, const LK &y)
		{
			return compare(x, y) ? phmap::weak_ordering::less
			       : compare(y, x) ? phmap::weak_ordering::greater
			       : phmap::weak_ordering::equivalent;
		}

	}  // namespace compare_internal
}


namespace phmap {

	namespace priv {

// A helper class that indicates if the Compare parameter is a key-compare-to
// comparator.
		template <typename Compare, typename T>
		using btree_is_key_compare_to =
		    std::is_convertible<phmap::invoke_result_t<Compare, const T &, const T &>,
		    phmap::weak_ordering>;

		struct StringBtreeDefaultLess {
			using is_transparent = void;

			StringBtreeDefaultLess() = default;

			// Compatibility constructor.
			StringBtreeDefaultLess(std::less<std::string>) {}       // NOLINT
#if PHMAP_HAVE_STD_STRING_VIEW
			StringBtreeDefaultLess(std::less<std::string_view>) {}  // NOLINT
			StringBtreeDefaultLess(phmap::Less<std::string_view>) {}  // NOLINT

			phmap::weak_ordering operator()(const std::string_view &lhs,
			                                const std::string_view &rhs) const
			{
				return compare_internal::compare_result_as_ordering(lhs.compare(rhs));
			}
#else
			phmap::weak_ordering operator()(const std::string &lhs,
			                                const std::string &rhs) const
			{
				return compare_internal::compare_result_as_ordering(lhs.compare(rhs));
			}
#endif
		};

		struct StringBtreeDefaultGreater {
			using is_transparent = void;

			StringBtreeDefaultGreater() = default;

			StringBtreeDefaultGreater(std::greater<std::string>) {}       // NOLINT
#if PHMAP_HAVE_STD_STRING_VIEW
			StringBtreeDefaultGreater(std::greater<std::string_view>) {}  // NOLINT

			phmap::weak_ordering operator()(std::string_view lhs,
			                                std::string_view rhs) const
			{
				return compare_internal::compare_result_as_ordering(rhs.compare(lhs));
			}
#else
			phmap::weak_ordering operator()(const std::string &lhs,
			                                const std::string &rhs) const
			{
				return compare_internal::compare_result_as_ordering(rhs.compare(lhs));
			}
#endif
		};

// A helper class to convert a boolean comparison into a three-way "compare-to"
// comparison that returns a negative value to indicate less-than, zero to
// indicate equality and a positive value to indicate greater-than. This helper
// class is specialized for less<std::string>, greater<std::string>,
// less<std::string_view>, and greater<std::string_view>.
//
// key_compare_to_adapter is provided so that btree users
// automatically get the more efficient compare-to code when using common
// google string types with common comparison functors.
// These string-like specializations also turn on heterogeneous lookup by
// default.
		template <typename Compare>
		struct key_compare_to_adapter {
			using type = Compare;
		};

		template <>
		struct key_compare_to_adapter<std::less<std::string>> {
			using type = StringBtreeDefaultLess;
		};

		template <>
		struct key_compare_to_adapter<phmap::Less<std::string>> {
			using type = StringBtreeDefaultLess;
		};

		template <>
		struct key_compare_to_adapter<std::greater<std::string>> {
			using type = StringBtreeDefaultGreater;
		};

#if PHMAP_HAVE_STD_STRING_VIEW
		template <>
		struct key_compare_to_adapter<std::less<std::string_view>> {
			using type = StringBtreeDefaultLess;
		};

		template <>
		struct key_compare_to_adapter<phmap::Less<std::string_view>> {
			using type = StringBtreeDefaultLess;
		};

		template <>
		struct key_compare_to_adapter<std::greater<std::string_view>> {
			using type = StringBtreeDefaultGreater;
		};
#endif

		template <typename Key, typename Compare, typename Alloc, int TargetNodeSize,
		          bool Multi, typename SlotPolicy>
		struct common_params {
			// If Compare is a common comparator for a std::string-like type, then we adapt it
			// to use heterogeneous lookup and to be a key-compare-to comparator.
			using key_compare = typename key_compare_to_adapter<Compare>::type;
			// A type which indicates if we have a key-compare-to functor or a plain old
			// key-compare functor.
			using is_key_compare_to = btree_is_key_compare_to<key_compare, Key>;

			using allocator_type = Alloc;
			using key_type = Key;
			using size_type = std::size_t ;
			using difference_type = ptrdiff_t;

			// True if this is a multiset or multimap.
			using is_multi_container = std::integral_constant<bool, Multi>;

			using slot_policy = SlotPolicy;
			using slot_type = typename slot_policy::slot_type;
			using value_type = typename slot_policy::value_type;
			using init_type = typename slot_policy::mutable_value_type;
			using pointer = value_type *;
			using const_pointer = const value_type *;
			using reference = value_type &;
			using const_reference = const value_type &;

			enum {
				kTargetNodeSize = TargetNodeSize,

				// Upper bound for the available space for values. This is largest for leaf
				// nodes, which have overhead of at least a pointer + 4 bytes (for storing
				// 3 field_types and an enum).
				kNodeSlotSpace =
				    TargetNodeSize - /*minimum overhead=*/(sizeof(void *) + 4),
			};

			// This is an integral type large enough to hold as many
			// ValueSize-values as will fit a node of TargetNodeSize bytes.
			using node_count_type =
			    phmap::conditional_t<(kNodeSlotSpace / sizeof(slot_type) >
			                          (std::numeric_limits<uint8_t>::max)()),
			    uint16_t, uint8_t>;  // NOLINT

			// The following methods are necessary for passing this struct as PolicyTraits
			// for node_handle and/or are used within btree.
			static value_type &element(slot_type *slot)
			{
				return slot_policy::element(slot);
			}
			static const value_type &element(const slot_type *slot)
			{
				return slot_policy::element(slot);
			}
			template <class... Args>
			static void construct(Alloc *alloc, slot_type *slot, Args &&... args)
			{
				slot_policy::construct(alloc, slot, std::forward<Args>(args)...);
			}
			static void construct(Alloc *alloc, slot_type *slot, slot_type *other)
			{
				slot_policy::construct(alloc, slot, other);
			}
			static void destroy(Alloc *alloc, slot_type *slot)
			{
				slot_policy::destroy(alloc, slot);
			}
			static void transfer(Alloc *alloc, slot_type *new_slot, slot_type *old_slot)
			{
				construct(alloc, new_slot, old_slot);
				destroy(alloc, old_slot);
			}
			static void swap(Alloc *alloc, slot_type *a, slot_type *b)
			{
				slot_policy::swap(alloc, a, b);
			}
			static void move(Alloc *alloc, slot_type *src, slot_type *dest)
			{
				slot_policy::move(alloc, src, dest);
			}
			static void move(Alloc *alloc, slot_type *first, slot_type *last,
			                 slot_type *result)
			{
				slot_policy::move(alloc, first, last, result);
			}
		};

// A parameters structure for holding the type parameters for a btree_map.
// Compare and Alloc should be nothrow copy-constructible.
		template <typename Key, typename Data, typename Compare, typename Alloc,
		          int TargetNodeSize, bool Multi>
		struct map_params : common_params<Key, Compare, Alloc, TargetNodeSize, Multi,
			phmap::priv::map_slot_policy<Key, Data>> {
			using super_type = typename map_params::common_params;
			using mapped_type = Data;
			// This type allows us to move keys when it is safe to do so. It is safe
			// for maps in which value_type and mutable_value_type are layout compatible.
			using slot_policy = typename super_type::slot_policy;
			using slot_type = typename super_type::slot_type;
			using value_type = typename super_type::value_type;
			using init_type = typename super_type::init_type;

			using key_compare = typename super_type::key_compare;
			// Inherit from key_compare for empty base class optimization.
			struct value_compare : private key_compare {
				value_compare() = default;
				explicit value_compare(const key_compare &cmp) : key_compare(cmp) {}

				template <typename T, typename U>
				auto operator()(const T &left, const U &right) const
				-> decltype(std::declval<key_compare>()(left.first, right.first))
				{
					return key_compare::operator()(left.first, right.first);
				}
			};
			using is_map_container = std::true_type;

			static const Key &key(const value_type &x)
			{
				return x.first;
			}
			static const Key &key(const init_type &x)
			{
				return x.first;
			}
			static const Key &key(const slot_type *x)
			{
				return slot_policy::key(x);
			}
			static mapped_type &value(value_type *value)
			{
				return value->second;
			}
		};

// This type implements the necessary functions from the
// btree::priv::slot_type interface.
		template <typename Key>
		struct set_slot_policy {
			using slot_type = Key;
			using value_type = Key;
			using mutable_value_type = Key;

			static value_type &element(slot_type *slot)
			{
				return *slot;
			}
			static const value_type &element(const slot_type *slot)
			{
				return *slot;
			}

			template <typename Alloc, class... Args>
			static void construct(Alloc *alloc, slot_type *slot, Args &&... args)
			{
				phmap::allocator_traits<Alloc>::construct(*alloc, slot,
				        std::forward<Args>(args)...);
			}

			template <typename Alloc>
			static void construct(Alloc *alloc, slot_type *slot, slot_type *other)
			{
				phmap::allocator_traits<Alloc>::construct(*alloc, slot, std::move(*other));
			}

			template <typename Alloc>
			static void destroy(Alloc *alloc, slot_type *slot)
			{
				phmap::allocator_traits<Alloc>::destroy(*alloc, slot);
			}

			template <typename Alloc>
			static void swap(Alloc * /*alloc*/, slot_type *a, slot_type *b)
			{
				using std::swap;
				swap(*a, *b);
			}

			template <typename Alloc>
			static void move(Alloc * /*alloc*/, slot_type *src, slot_type *dest)
			{
				*dest = std::move(*src);
			}

			template <typename Alloc>
			static void move(Alloc *alloc, slot_type *first, slot_type *last,
			                 slot_type *result)
			{
				for (slot_type *src = first, *dest = result; src != last; ++src, ++dest)
					move(alloc, src, dest);
			}
		};

// A parameters structure for holding the type parameters for a btree_set.
// Compare and Alloc should be nothrow copy-constructible.
		template <typename Key, typename Compare, typename Alloc, int TargetNodeSize,
		          bool Multi>
		struct set_params : common_params<Key, Compare, Alloc, TargetNodeSize, Multi,
			set_slot_policy<Key>> {
			using value_type = Key;
			using slot_type = typename set_params::common_params::slot_type;
			using value_compare = typename set_params::common_params::key_compare;
			using is_map_container = std::false_type;

			static const Key &key(const value_type &x)
			{
				return x;
			}
			static const Key &key(const slot_type *x)
			{
				return *x;
			}
		};

// An adapter class that converts a lower-bound compare into an upper-bound
// compare. Note: there is no need to make a version of this adapter specialized
// for key-compare-to functors because the upper-bound (the first value greater
// than the input) is never an exact match.
		template <typename Compare>
		struct upper_bound_adapter {
			explicit upper_bound_adapter(const Compare &c) : comp(c) {}
			template <typename K, typename LK>
			bool operator()(const K &a, const LK &b) const
			{
				// Returns true when a is not greater than b.
				return !phmap::compare_internal::compare_result_as_less_than(comp(b, a));
			}

		private:
			Compare comp;
		};

		enum class MatchKind : uint8_t { kEq, kNe };

		template <typename V, bool IsCompareTo>
		struct SearchResult {
			V value;
			MatchKind match;

			static constexpr bool HasMatch()
			{
				return true;
			}
			bool IsEq() const
			{
				return match == MatchKind::kEq;
			}
		};

// When we don't use CompareTo, `match` is not present.
// This ensures that callers can't use it accidentally when it provides no
// useful information.
		template <typename V>
		struct SearchResult<V, false> {
			V value;

			static constexpr bool HasMatch()
			{
				return false;
			}
			static constexpr bool IsEq()
			{
				return false;
			}
		};

// A node in the btree holding. The same node type is used for both internal
// and leaf nodes in the btree, though the nodes are allocated in such a way
// that the children array is only valid in internal nodes.
		template <typename Params>
		class btree_node {
			using is_key_compare_to = typename Params::is_key_compare_to;
			using is_multi_container = typename Params::is_multi_container;
			using field_type = typename Params::node_count_type;
			using allocator_type = typename Params::allocator_type;
			using slot_type = typename Params::slot_type;

		public:
			using params_type = Params;
			using key_type = typename Params::key_type;
			using value_type = typename Params::value_type;
			using pointer = typename Params::pointer;
			using const_pointer = typename Params::const_pointer;
			using reference = typename Params::reference;
			using const_reference = typename Params::const_reference;
			using key_compare = typename Params::key_compare;
			using size_type = typename Params::size_type;
			using difference_type = typename Params::difference_type;

			// Btree decides whether to use linear node search as follows:
			//   - If the key is arithmetic and the comparator is std::less or
			//     std::greater, choose linear.
			//   - Otherwise, choose binary.
			// TODO(ezb): Might make sense to add condition(s) based on node-size.
			using use_linear_search = std::integral_constant<
			                          bool,
			                          std::is_arithmetic<key_type>::value &&
			                          (std::is_same<phmap::Less<key_type>, key_compare>::value ||
			                           std::is_same<std::less<key_type>, key_compare>::value ||
			                           std::is_same<std::greater<key_type>, key_compare>::value)>;


			~btree_node() = default;
			btree_node(btree_node const &) = delete;
			btree_node &operator=(btree_node const &) = delete;

			// Public for EmptyNodeType.
			constexpr static size_type Alignment()
			{
				static_assert(LeafLayout(1).Alignment() == InternalLayout().Alignment(),
				              "Alignment of all nodes must be equal.");
				return (size_type)InternalLayout().Alignment();
			}

		protected:
			btree_node() = default;

		private:
			using layout_type = phmap::priv::Layout<btree_node *, field_type,
			      slot_type, btree_node *>;
			constexpr static size_type SizeWithNValues(size_type n)
			{
				return (size_type)layout_type(/*parent*/ 1,
				        /*position, start, count, max_count*/ 4,
				        /*values*/ (size_t)n,
				        /*children*/ 0)
				       .AllocSize();
			}
			// A lower bound for the overhead of fields other than values in a leaf node.
			constexpr static size_type MinimumOverhead()
			{
				return (size_type)(SizeWithNValues(1) - sizeof(value_type));
			}

			// Compute how many values we can fit onto a leaf node taking into account
			// padding.
			constexpr static size_type NodeTargetValues(const int begin, const int end)
			{
				return begin == end ? begin
				       : SizeWithNValues((begin + end) / 2 + 1) >
				       params_type::kTargetNodeSize
				       ? NodeTargetValues(begin, (begin + end) / 2)
				       : NodeTargetValues((begin + end) / 2 + 1, end);
			}

			enum {
				kTargetNodeSize = params_type::kTargetNodeSize,
				kNodeTargetValues = NodeTargetValues(0, params_type::kTargetNodeSize),

				// We need a minimum of 3 values per internal node in order to perform
				// splitting (1 value for the two nodes involved in the split and 1 value
				// propagated to the parent as the delimiter for the split).
				kNodeValues = kNodeTargetValues >= 3 ? kNodeTargetValues : 3,

				// The node is internal (i.e. is not a leaf node) if and only if `max_count`
				// has this value.
				kInternalNodeMaxCount = 0,
			};

			// Leaves can have less than kNodeValues values.
			constexpr static layout_type LeafLayout(const int max_values = kNodeValues)
			{
				return layout_type(/*parent*/ 1,
				                              /*position, start, count, max_count*/ 4,
				                              /*values*/ (size_t)max_values,
				                              /*children*/ 0);
			}
			constexpr static layout_type InternalLayout()
			{
				return layout_type(/*parent*/ 1,
				                              /*position, start, count, max_count*/ 4,
				                              /*values*/ kNodeValues,
				                              /*children*/ kNodeValues + 1);
			}
			constexpr static size_type LeafSize(const int max_values = kNodeValues)
			{
				return (size_type)LeafLayout(max_values).AllocSize();
			}
			constexpr static size_type InternalSize()
			{
				return (size_type)InternalLayout().AllocSize();
			}

			// N is the index of the type in the Layout definition.
			// ElementType<N> is the Nth type in the Layout definition.
			template <size_type N>
			inline typename layout_type::template ElementType<N> *GetField()
			{
				// We assert that we don't read from values that aren't there.
				assert(N < 3 || !leaf());
				return InternalLayout().template Pointer<N>(reinterpret_cast<char *>(this));
			}

			template <size_type N>
			inline const typename layout_type::template ElementType<N> *GetField() const
			{
				assert(N < 3 || !leaf());
				return InternalLayout().template Pointer<N>(
				           reinterpret_cast<const char *>(this));
			}

			void set_parent(btree_node *p)
			{
				*GetField<0>() = p;
			}
			field_type &mutable_count()
			{
				return GetField<1>()[2];
			}
			slot_type *slot(size_type i)
			{
				return &GetField<2>()[i];
			}
			const slot_type *slot(size_type i) const
			{
				return &GetField<2>()[i];
			}
			void set_position(field_type v)
			{
				GetField<1>()[0] = v;
			}
			void set_start(field_type v)
			{
				GetField<1>()[1] = v;
			}
			void set_count(field_type v)
			{
				GetField<1>()[2] = v;
			}
			void set_max_count(field_type v)
			{
				GetField<1>()[3] = v;
			}

		public:
			// Whether this is a leaf node or not. This value doesn't change after the
			// node is created.
			bool leaf() const
			{
				return GetField<1>()[3] != kInternalNodeMaxCount;
			}

			// Getter for the position of this node in its parent.
			field_type position() const
			{
				return GetField<1>()[0];
			}

			// Getter for the offset of the first value in the `values` array.
			field_type start() const
			{
				return GetField<1>()[1];
			}

			// Getters for the number of values stored in this node.
			field_type count() const
			{
				return GetField<1>()[2];
			}
			field_type max_count() const
			{
				// Internal nodes have max_count==kInternalNodeMaxCount.
				// Leaf nodes have max_count in [1, kNodeValues].
				const field_type max_cnt = GetField<1>()[3];
				return max_cnt == field_type{kInternalNodeMaxCount}
				       ? field_type{kNodeValues}
				       :
				       max_cnt;
			}

			// Getter for the parent of this node.
			btree_node *parent() const
			{
				return *GetField<0>();
			}
			// Getter for whether the node is the root of the tree. The parent of the
			// root of the tree is the leftmost node in the tree which is guaranteed to
			// be a leaf.
			bool is_root() const
			{
				return parent()->leaf();
			}
			void make_root()
			{
				assert(parent()->is_root());
				set_parent(parent()->parent());
			}

			// Getters for the key/value at position i in the node.
			const key_type &key(size_type i) const
			{
				return params_type::key(slot(i));
			}
			reference value(size_type i)
			{
				return params_type::element(slot(i));
			}
			const_reference value(size_type i) const
			{
				return params_type::element(slot(i));
			}

#if defined(__GNUC__) || defined(__clang__)
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Warray-bounds"
#endif
			// Getters/setter for the child at position i in the node.
			btree_node *child(size_type i) const
			{
				return GetField<3>()[i];
			}
			btree_node *&mutable_child(size_type i)
			{
				return GetField<3>()[i];
			}
			void clear_child(size_type i)
			{
				phmap::priv::SanitizerPoisonObject(&mutable_child(i));
			}
			void set_child(size_type i, btree_node *c)
			{
				phmap::priv::SanitizerUnpoisonObject(&mutable_child(i));
				mutable_child(i) = c;
				c->set_position((field_type)i);
			}
#if defined(__GNUC__) || defined(__clang__)
#pragma GCC diagnostic pop
#endif
			void init_child(int i, btree_node *c)
			{
				set_child(i, c);
				c->set_parent(this);
			}

			// Returns the position of the first value whose key is not less than k.
			template <typename K>
			SearchResult<int, is_key_compare_to::value> lower_bound(
			    const K &k, const key_compare &comp) const
			{
				return use_linear_search::value ? linear_search(k, comp)
				       : binary_search(k, comp);
			}
			// Returns the position of the first value whose key is greater than k.
			template <typename K>
			int upper_bound(const K &k, const key_compare &comp) const
			{
				auto upper_compare = upper_bound_adapter<key_compare>(comp);
				return use_linear_search::value ? linear_search(k, upper_compare).value
				       : binary_search(k, upper_compare).value;
			}

			template <typename K, typename Compare>
			SearchResult<int, btree_is_key_compare_to<Compare, key_type>::value>
			linear_search(const K &k, const Compare &comp) const
			{
				return linear_search_impl(k, 0, count(), comp,
				                          btree_is_key_compare_to<Compare, key_type>());
			}

			template <typename K, typename Compare>
			SearchResult<int, btree_is_key_compare_to<Compare, key_type>::value>
			binary_search(const K &k, const Compare &comp) const
			{
				return binary_search_impl(k, 0, count(), comp,
				                          btree_is_key_compare_to<Compare, key_type>());
			}

			// Returns the position of the first value whose key is not less than k using
			// linear search performed using plain compare.
			template <typename K, typename Compare>
			SearchResult<int, false> linear_search_impl(
			    const K &k, int s, const int e, const Compare &comp,
			    std::false_type /* IsCompareTo */) const
			{
				while (s < e) {
					if (!comp(key(s), k)) {
						break;
					}
					++s;
				}
				return {s};
			}

			// Returns the position of the first value whose key is not less than k using
			// linear search performed using compare-to.
			template <typename K, typename Compare>
			SearchResult<int, true> linear_search_impl(
			    const K &k, int s, const int e, const Compare &comp,
			    std::true_type /* IsCompareTo */) const
			{
				while (s < e) {
					const phmap::weak_ordering c = comp(key(s), k);
					if (c == 0) {
						return {s, MatchKind::kEq};
					}
					else if (c > 0) {
						break;
					}
					++s;
				}
				return {s, MatchKind::kNe};
			}

			// Returns the position of the first value whose key is not less than k using
			// binary search performed using plain compare.
			template <typename K, typename Compare>
			SearchResult<int, false> binary_search_impl(
			    const K &k, int s, int e, const Compare &comp,
			    std::false_type /* IsCompareTo */) const
			{
				while (s != e) {
					const int mid = (s + e) >> 1;
					if (comp(key(mid), k)) {
						s = mid + 1;
					}
					else {
						e = mid;
					}
				}
				return {s};
			}

			// Returns the position of the first value whose key is not less than k using
			// binary search performed using compare-to.
			template <typename K, typename CompareTo>
			SearchResult<int, true> binary_search_impl(
			    const K &k, int s, int e, const CompareTo &comp,
			    std::true_type /* IsCompareTo */) const
			{
				if (is_multi_container::value) {
					MatchKind exact_match = MatchKind::kNe;
					while (s != e) {
						const int mid = (s + e) >> 1;
						const phmap::weak_ordering c = comp(key(mid), k);
						if (c < 0) {
							s = mid + 1;
						}
						else {
							e = mid;
							if (c == 0) {
								// Need to return the first value whose key is not less than k,
								// which requires continuing the binary search if this is a
								// multi-container.
								exact_match = MatchKind::kEq;
							}
						}
					}
					return {s, exact_match};
				}
				else {    // Not a multi-container.
					while (s != e) {
						const int mid = (s + e) >> 1;
						const phmap::weak_ordering c = comp(key(mid), k);
						if (c < 0) {
							s = mid + 1;
						}
						else if (c > 0) {
							e = mid;
						}
						else {
							return {mid, MatchKind::kEq};
						}
					}
					return {s, MatchKind::kNe};
				}
			}

			// Emplaces a value at position i, shifting all existing values and
			// children at positions >= i to the right by 1.
			template <typename... Args>
			void emplace_value(size_type i, allocator_type *alloc, Args &&... args);

			// Removes the value at position i, shifting all existing values and children
			// at positions > i to the left by 1.
			void remove_value(int i, allocator_type *alloc);

			// Removes the values at positions [i, i + to_erase), shifting all values
			// after that range to the left by to_erase. Does not change children at all.
			void remove_values_ignore_children(int i, size_type to_erase,
			                                   allocator_type *alloc);

			// Rebalances a node with its right sibling.
			void rebalance_right_to_left(int to_move, btree_node *right,
			                             allocator_type *alloc);
			void rebalance_left_to_right(int to_move, btree_node *right,
			                             allocator_type *alloc);

			// Splits a node, moving a portion of the node's values to its right sibling.
			void split(int insert_position, btree_node *dest, allocator_type *alloc);

			// Merges a node with its right sibling, moving all of the values and the
			// delimiting key in the parent node onto itself.
			void merge(btree_node *sibling, allocator_type *alloc);

			// Swap the contents of "this" and "src".
			void swap(btree_node *src, allocator_type *alloc);

			// Node allocation/deletion routines.
			static btree_node *init_leaf(btree_node *n, btree_node *parent,
			                             int max_cnt)
			{
				n->set_parent(parent);
				n->set_position(0);
				n->set_start(0);
				n->set_count(0);
				n->set_max_count((field_type)max_cnt);
				phmap::priv::SanitizerPoisonMemoryRegion(
				    n->slot(0), max_cnt * sizeof(slot_type));
				return n;
			}
			static btree_node *init_internal(btree_node *n, btree_node *parent)
			{
				init_leaf(n, parent, kNodeValues);
				// Set `max_count` to a sentinel value to indicate that this node is
				// internal.
				n->set_max_count(kInternalNodeMaxCount);
				phmap::priv::SanitizerPoisonMemoryRegion(
				    &n->mutable_child(0), (kNodeValues + 1) * sizeof(btree_node *));
				return n;
			}
			void destroy(allocator_type *alloc)
			{
				for (int i = 0; i < count(); ++i) {
					value_destroy(i, alloc);
				}
			}

		public:
			// Exposed only for tests.
			static bool testonly_uses_linear_node_search()
			{
				return use_linear_search::value;
			}

		private:
			template <typename... Args>
			void value_init(const size_type i, allocator_type *alloc, Args &&... args)
			{
				phmap::priv::SanitizerUnpoisonObject(slot(i));
				params_type::construct(alloc, slot(i), std::forward<Args>(args)...);
			}
			void value_destroy(const size_type i, allocator_type *alloc)
			{
				params_type::destroy(alloc, slot(i));
				phmap::priv::SanitizerPoisonObject(slot(i));
			}

			// Move n values starting at value i in this node into the values starting at
			// value j in node x.
			void uninitialized_move_n(const size_type n, const size_type i,
			                          const size_type j, btree_node *x,
			                          allocator_type *alloc)
			{
				phmap::priv::SanitizerUnpoisonMemoryRegion(
				    x->slot(j), n * sizeof(slot_type));
				for (slot_type *src = slot(i), *end = src + n, *dest = x->slot(j);
				        src != end; ++src, ++dest) {
					params_type::construct(alloc, dest, src);
				}
			}

			// Destroys a range of n values, starting at index i.
			void value_destroy_n(const size_type i, const size_type n,
			                     allocator_type *alloc)
			{
				for (size_type j = 0; j < n; ++j) {
					value_destroy(i + j, alloc);
				}
			}

			template <typename P>
			friend class btree;
			template <typename N, typename R, typename P>
			friend struct btree_iterator;
			friend class BtreeNodePeer;
		};

		template <typename Node, typename Reference, typename Pointer>
		struct btree_iterator {
		private:
			using key_type = typename Node::key_type;
			using size_type = typename Node::size_type;
			using params_type = typename Node::params_type;

			using node_type = Node;
			using normal_node = typename std::remove_const<Node>::type;
			using const_node = const Node;
			using normal_pointer = typename params_type::pointer;
			using normal_reference = typename params_type::reference;
			using const_pointer = typename params_type::const_pointer;
			using const_reference = typename params_type::const_reference;
			using slot_type = typename params_type::slot_type;

			using iterator =
			    btree_iterator<normal_node, normal_reference, normal_pointer>;
			using const_iterator =
			    btree_iterator<const_node, const_reference, const_pointer>;

		public:
			// These aliases are public for std::iterator_traits.
			using difference_type = typename Node::difference_type;
			using value_type = typename params_type::value_type;
			using pointer = Pointer;
			using reference = Reference;
			using iterator_category = std::bidirectional_iterator_tag;

			btree_iterator() : node(nullptr), position(-1) {}
			btree_iterator(Node *n, int p) : node(n), position(p) {}

			// NOTE: this SFINAE allows for implicit conversions from iterator to
			// const_iterator, but it specifically avoids defining copy constructors so
			// that btree_iterator can be trivially copyable. This is for performance and
			// binary size reasons.
			template <typename N, typename R, typename P,
			          phmap::enable_if_t<
			              std::is_same<btree_iterator<N, R, P>, iterator>::value &&
			              std::is_same<btree_iterator, const_iterator>::value,
			              int> = 0>
			btree_iterator(const btree_iterator<N, R, P> &x)  // NOLINT
				: node(x.node), position(x.position) {}

		private:
			// This SFINAE allows explicit conversions from const_iterator to
			// iterator, but also avoids defining a copy constructor.
			// NOTE: the const_cast is safe because this constructor is only called by
			// non-const methods and the container owns the nodes.
			template <typename N, typename R, typename P,
			          phmap::enable_if_t<
			              std::is_same<btree_iterator<N, R, P>, const_iterator>::value &&
			              std::is_same<btree_iterator, iterator>::value,
			              int> = 0>
			explicit btree_iterator(const btree_iterator<N, R, P> &x)
				: node(const_cast<node_type *>(x.node)), position(x.position) {}

			// Increment/decrement the iterator.
			void increment()
			{
				if (node->leaf() && ++position < node->count()) {
					return;
				}
				increment_slow();
			}
			void increment_slow();

			void decrement()
			{
				if (node->leaf() && --position >= 0) {
					return;
				}
				decrement_slow();
			}
			void decrement_slow();

		public:
			bool operator==(const const_iterator &x) const
			{
				return node == x.node && position == x.position;
			}
			bool operator!=(const const_iterator &x) const
			{
				return node != x.node || position != x.position;
			}
			bool operator==(const iterator &x) const
			{
				return node == x.node && position == x.position;
			}
			bool operator!=(const iterator &x) const
			{
				return node != x.node || position != x.position;
			}

			// Accessors for the key/value the iterator is pointing at.
			reference operator*() const
			{
				return node->value(position);
			}
			pointer operator->() const
			{
				return &node->value(position);
			}

			btree_iterator& operator++()
			{
				increment();
				return *this;
			}
			btree_iterator& operator--()
			{
				decrement();
				return *this;
			}
			btree_iterator operator++(int)
			{
				btree_iterator tmp = *this;
				++*this;
				return tmp;
			}
			btree_iterator operator--(int)
			{
				btree_iterator tmp = *this;
				--*this;
				return tmp;
			}

		private:
			template <typename Params>
			friend class btree;
			template <typename Tree>
			friend class btree_container;
			template <typename Tree>
			friend class btree_set_container;
			template <typename Tree>
			friend class btree_map_container;
			template <typename Tree>
			friend class btree_multiset_container;
			template <typename N, typename R, typename P>
			friend struct btree_iterator;
			template <typename TreeType, typename CheckerType>
			friend class base_checker;

			const key_type &key() const
			{
				return node->key(position);
			}
			slot_type *slot()
			{
				return node->slot(position);
			}

			// The node in the tree the iterator is pointing at.
			Node *node;
			// The position within the node of the tree the iterator is pointing at.
			// TODO(ezb): make this a field_type
			int position;
		};

		template <typename Params>
		class btree {
			using node_type = btree_node<Params>;
			using is_key_compare_to = typename Params::is_key_compare_to;

			// We use a static empty node for the root/leftmost/rightmost of empty btrees
			// in order to avoid branching in begin()/end().
		struct alignas(node_type::Alignment()) EmptyNodeType : node_type {
				using field_type = typename node_type::field_type;
				node_type *parent;
				field_type position = 0;
				field_type start = 0;
				field_type count = 0;
				// max_count must be != kInternalNodeMaxCount (so that this node is regarded
				// as a leaf node). max_count() is never called when the tree is empty.
				field_type max_count = node_type::kInternalNodeMaxCount + 1;

#ifdef _MSC_VER
				// MSVC has constexpr code generations bugs here.
				EmptyNodeType() : parent(this) {}
#else
				constexpr EmptyNodeType(node_type *p) : parent(p) {}
#endif
			};

			static node_type *EmptyNode()
			{
#ifdef _MSC_VER
				static EmptyNodeType empty_node;
				// This assert fails on some other construction methods.
				assert(empty_node.parent == &empty_node);
				return &empty_node;
#else
				static constexpr EmptyNodeType empty_node(
				    const_cast<EmptyNodeType *>(&empty_node));
				return const_cast<EmptyNodeType *>(&empty_node);
#endif
			}

			enum {
				kNodeValues = node_type::kNodeValues,
				kMinNodeValues = kNodeValues / 2,
			};

			struct node_stats {
				using size_type = typename Params::size_type;

				node_stats(size_type l, size_type i)
					: leaf_nodes(l),
					  internal_nodes(i)
				{
				}

				node_stats& operator+=(const node_stats &x)
				{
					leaf_nodes += x.leaf_nodes;
					internal_nodes += x.internal_nodes;
					return *this;
				}

				size_type leaf_nodes;
				size_type internal_nodes;
			};

		public:
			using key_type = typename Params::key_type;
			using value_type = typename Params::value_type;
			using size_type = typename Params::size_type;
			using difference_type = typename Params::difference_type;
			using key_compare = typename Params::key_compare;
			using value_compare = typename Params::value_compare;
			using allocator_type = typename Params::allocator_type;
			using reference = typename Params::reference;
			using const_reference = typename Params::const_reference;
			using pointer = typename Params::pointer;
			using const_pointer = typename Params::const_pointer;
			using iterator = btree_iterator<node_type, reference, pointer>;
			using const_iterator = typename iterator::const_iterator;
			using reverse_iterator = std::reverse_iterator<iterator>;
			using const_reverse_iterator = std::reverse_iterator<const_iterator>;
			using node_handle_type = node_handle<Params, Params, allocator_type>;

			// Internal types made public for use by btree_container types.
			using params_type = Params;
			using slot_type = typename Params::slot_type;

		private:
			// For use in copy_or_move_values_in_order.
			const value_type &maybe_move_from_iterator(const_iterator x)
			{
				return *x;
			}
			value_type &&maybe_move_from_iterator(iterator x)
			{
				return std::move(*x);
			}

			// Copies or moves (depending on the template parameter) the values in
			// x into this btree in their order in x. This btree must be empty before this
			// method is called. This method is used in copy construction, copy
			// assignment, and move assignment.
			template <typename Btree>
			void copy_or_move_values_in_order(Btree *x);

			// Validates that various assumptions/requirements are true at compile time.
			constexpr static bool static_assert_validation();

		public:
			btree(const key_compare &comp, const allocator_type &alloc);

			btree(const btree &x);
			btree(btree &&x) noexcept
				: root_(std::move(x.root_)),
				  rightmost_(phmap::exchange(x.rightmost_, EmptyNode())),
				  size_(phmap::exchange(x.size_, 0))
			{
				x.mutable_root() = EmptyNode();
			}

			~btree()
			{
				// Put static_asserts in destructor to avoid triggering them before the type
				// is complete.
				static_assert(static_assert_validation(), "This call must be elided.");
				clear();
			}

			// Assign the contents of x to *this.
			btree &operator=(const btree &x);
			btree &operator=(btree &&x) noexcept;

			iterator begin()
			{
				return iterator(leftmost(), 0);
			}
			const_iterator begin() const
			{
				return const_iterator(leftmost(), 0);
			}
			iterator end()
			{
				return iterator(rightmost_, rightmost_->count());
			}
			const_iterator end() const
			{
				return const_iterator(rightmost_, rightmost_->count());
			}
			reverse_iterator rbegin()
			{
				return reverse_iterator(end());
			}
			const_reverse_iterator rbegin() const
			{
				return const_reverse_iterator(end());
			}
			reverse_iterator rend()
			{
				return reverse_iterator(begin());
			}
			const_reverse_iterator rend() const
			{
				return const_reverse_iterator(begin());
			}

			// Finds the first element whose key is not less than key.
			template <typename K>
			iterator lower_bound(const K &key)
			{
				return internal_end(internal_lower_bound(key));
			}
			template <typename K>
			const_iterator lower_bound(const K &key) const
			{
				return internal_end(internal_lower_bound(key));
			}

			// Finds the first element whose key is greater than key.
			template <typename K>
			iterator upper_bound(const K &key)
			{
				return internal_end(internal_upper_bound(key));
			}
			template <typename K>
			const_iterator upper_bound(const K &key) const
			{
				return internal_end(internal_upper_bound(key));
			}

			// Finds the range of values which compare equal to key. The first member of
			// the returned pair is equal to lower_bound(key). The second member pair of
			// the pair is equal to upper_bound(key).
			template <typename K>
			std::pair<iterator, iterator> equal_range(const K &key)
			{
				return {lower_bound(key), upper_bound(key)};
			}
			template <typename K>
			std::pair<const_iterator, const_iterator> equal_range(const K &key) const
			{
				return {lower_bound(key), upper_bound(key)};
			}

			// Inserts a value into the btree only if it does not already exist. The
			// boolean return value indicates whether insertion succeeded or failed.
			// Requirement: if `key` already exists in the btree, does not consume `args`.
			// Requirement: `key` is never referenced after consuming `args`.
			template <typename... Args>
			std::pair<iterator, bool> insert_unique(const key_type &key, Args &&... args);

			// Inserts with hint. Checks to see if the value should be placed immediately
			// before `position` in the tree. If so, then the insertion will take
			// amortized constant time. If not, the insertion will take amortized
			// logarithmic time as if a call to insert_unique() were made.
			// Requirement: if `key` already exists in the btree, does not consume `args`.
			// Requirement: `key` is never referenced after consuming `args`.
			template <typename... Args>
			std::pair<iterator, bool> insert_hint_unique(iterator position,
			        const key_type &key,
			        Args &&... args);

			// Insert a range of values into the btree.
			template <typename InputIterator>
			void insert_iterator_unique(InputIterator b, InputIterator e);

			// Inserts a value into the btree.
			template <typename ValueType>
			iterator insert_multi(const key_type &key, ValueType &&v);

			// Inserts a value into the btree.
			template <typename ValueType>
			iterator insert_multi(ValueType &&v)
			{
				return insert_multi(params_type::key(v), std::forward<ValueType>(v));
			}

			// Insert with hint. Check to see if the value should be placed immediately
			// before position in the tree. If it does, then the insertion will take
			// amortized constant time. If not, the insertion will take amortized
			// logarithmic time as if a call to insert_multi(v) were made.
			template <typename ValueType>
			iterator insert_hint_multi(iterator position, ValueType &&v);

			// Insert a range of values into the btree.
			template <typename InputIterator>
			void insert_iterator_multi(InputIterator b, InputIterator e);

			// Erase the specified iterator from the btree. The iterator must be valid
			// (i.e. not equal to end()).  Return an iterator pointing to the node after
			// the one that was erased (or end() if none exists).
			// Requirement: does not read the value at `*iter`.
			iterator erase(iterator iter);

			// Erases range. Returns the number of keys erased and an iterator pointing
			// to the element after the last erased element.
			std::pair<size_type, iterator> erase(iterator begin, iterator end);

			// Erases the specified key from the btree. Returns 1 if an element was
			// erased and 0 otherwise.
			template <typename K>
			size_type erase_unique(const K &key);

			// Erases all of the entries matching the specified key from the
			// btree. Returns the number of elements erased.
			template <typename K>
			size_type erase_multi(const K &key);

			// Finds the iterator corresponding to a key or returns end() if the key is
			// not present.
			template <typename K>
			iterator find(const K &key)
			{
				return internal_end(internal_find(key));
			}
			template <typename K>
			const_iterator find(const K &key) const
			{
				return internal_end(internal_find(key));
			}

			// Returns a count of the number of times the key appears in the btree.
			template <typename K>
			size_type count_unique(const K &key) const
			{
				const iterator beg = internal_find(key);
				if (beg.node == nullptr) {
					// The key doesn't exist in the tree.
					return 0;
				}
				return 1;
			}
			// Returns a count of the number of times the key appears in the btree.
			template <typename K>
			size_type count_multi(const K &key) const
			{
				const auto range = equal_range(key);
				return std::distance(range.first, range.second);
			}

			// Clear the btree, deleting all of the values it contains.
			void clear();

			// Swap the contents of *this and x.
			void swap(btree &x);

			const key_compare &key_comp() const noexcept
			{
				return root_.template get<0>();
			}
			template <typename K, typename LK>
			bool compare_keys(const K &x, const LK &y) const
			{
				return compare_internal::compare_result_as_less_than(key_comp()(x, y));
			}

			value_compare value_comp() const
			{
				return value_compare(key_comp());
			}

			// Verifies the structure of the btree.
			void verify() const;

			// Size routines.
			size_type size() const
			{
				return size_;
			}
			size_type max_size() const
			{
				return (std::numeric_limits<size_type>::max)();
			}
			bool empty() const
			{
				return size_ == 0;
			}

			// The height of the btree. An empty tree will have height 0.
			size_type height() const
			{
				size_type h = 0;
				if (!empty()) {
					// Count the length of the chain from the leftmost node up to the
					// root. We actually count from the root back around to the level below
					// the root, but the calculation is the same because of the circularity
					// of that traversal.
					const node_type *n = root();
					do {
						++h;
						n = n->parent();
					}
					while (n != root());
				}
				return h;
			}

			// The number of internal, leaf and total nodes used by the btree.
			size_type leaf_nodes() const
			{
				return internal_stats(root()).leaf_nodes;
			}
			size_type internal_nodes() const
			{
				return internal_stats(root()).internal_nodes;
			}
			size_type nodes() const
			{
				node_stats stats = internal_stats(root());
				return stats.leaf_nodes + stats.internal_nodes;
			}

			// The total number of bytes used by the btree.
			size_type bytes_used() const
			{
				node_stats stats = internal_stats(root());
				if (stats.leaf_nodes == 1 && stats.internal_nodes == 0) {
					return sizeof(*this) +
					       node_type::LeafSize(root()->max_count());
				}
				else {
					return sizeof(*this) +
					       stats.leaf_nodes * node_type::LeafSize() +
					       stats.internal_nodes * node_type::InternalSize();
				}
			}

			// The average number of bytes used per value stored in the btree.
			static double average_bytes_per_value()
			{
				// Returns the number of bytes per value on a leaf node that is 75%
				// full. Experimentally, this matches up nicely with the computed number of
				// bytes per value in trees that had their values inserted in random order.
				return node_type::LeafSize() / (kNodeValues * 0.75);
			}

			// The fullness of the btree. Computed as the number of elements in the btree
			// divided by the maximum number of elements a tree with the current number
			// of nodes could hold. A value of 1 indicates perfect space
			// utilization. Smaller values indicate space wastage.
			// Returns 0 for empty trees.
			double fullness() const
			{
				if (empty()) return 0.0;
				return static_cast<double>(size()) / (nodes() * kNodeValues);
			}
			// The overhead of the btree structure in bytes per node. Computed as the
			// total number of bytes used by the btree minus the number of bytes used for
			// storing elements divided by the number of elements.
			// Returns 0 for empty trees.
			double overhead() const
			{
				if (empty()) return 0.0;
				return (bytes_used() - size() * sizeof(value_type)) /
				       static_cast<double>(size());
			}

			// The allocator used by the btree.
			allocator_type get_allocator() const
			{
				return allocator();
			}

		private:
			// Internal accessor routines.
			node_type *root()
			{
				return root_.template get<2>();
			}
			const node_type *root() const
			{
				return root_.template get<2>();
			}
			node_type *&mutable_root() noexcept
			{
				return root_.template get<2>();
			}
			key_compare *mutable_key_comp() noexcept
			{
				return &root_.template get<0>();
			}

			// The leftmost node is stored as the parent of the root node.
			node_type *leftmost()
			{
				return root()->parent();
			}
			const node_type *leftmost() const
			{
				return root()->parent();
			}

			// Allocator routines.
			allocator_type *mutable_allocator() noexcept
			{
				return &root_.template get<1>();
			}
			const allocator_type &allocator() const noexcept
			{
				return root_.template get<1>();
			}

			// Allocates a correctly aligned node of at least size bytes using the
			// allocator.
			node_type *allocate(const size_type sz)
			{
				return reinterpret_cast<node_type *>(
				           phmap::priv::Allocate<node_type::Alignment()>(
				               mutable_allocator(), (size_t)sz));
			}

			// Node creation/deletion routines.
			node_type* new_internal_node(node_type *parent)
			{
				node_type *p = allocate(node_type::InternalSize());
				return node_type::init_internal(p, parent);
			}
			node_type* new_leaf_node(node_type *parent)
			{
				node_type *p = allocate(node_type::LeafSize());
				return node_type::init_leaf(p, parent, kNodeValues);
			}
			node_type *new_leaf_root_node(const int max_count)
			{
				node_type *p = allocate(node_type::LeafSize(max_count));
				return node_type::init_leaf(p, p, max_count);
			}

			// Deletion helper routines.
			void erase_same_node(iterator begin, iterator end);
			iterator erase_from_leaf_node(iterator begin, size_type to_erase);
			iterator rebalance_after_delete(iterator iter);

			// Deallocates a node of a certain size in bytes using the allocator.
			void deallocate(const size_type sz, node_type *node)
			{
				phmap::priv::Deallocate<node_type::Alignment()>(
				    mutable_allocator(), node, (size_t)sz);
			}

			void delete_internal_node(node_type *node)
			{
				node->destroy(mutable_allocator());
				deallocate(node_type::InternalSize(), node);
			}
			void delete_leaf_node(node_type *node)
			{
				node->destroy(mutable_allocator());
				deallocate(node_type::LeafSize(node->max_count()), node);
			}

			// Rebalances or splits the node iter points to.
			void rebalance_or_split(iterator *iter);

			// Merges the values of left, right and the delimiting key on their parent
			// onto left, removing the delimiting key and deleting right.
			void merge_nodes(node_type *left, node_type *right);

			// Tries to merge node with its left or right sibling, and failing that,
			// rebalance with its left or right sibling. Returns true if a merge
			// occurred, at which point it is no longer valid to access node. Returns
			// false if no merging took place.
			bool try_merge_or_rebalance(iterator *iter);

			// Tries to shrink the height of the tree by 1.
			void try_shrink();

			iterator internal_end(iterator iter)
			{
				return iter.node != nullptr ? iter : end();
			}
			const_iterator internal_end(const_iterator iter) const
			{
				return iter.node != nullptr ? iter : end();
			}

			// Emplaces a value into the btree immediately before iter. Requires that
			// key(v) <= iter.key() and (--iter).key() <= key(v).
			template <typename... Args>
			iterator internal_emplace(iterator iter, Args &&... args);

			// Returns an iterator pointing to the first value >= the value "iter" is
			// pointing at. Note that "iter" might be pointing to an invalid location as
			// iter.position == iter.node->count(). This routine simply moves iter up in
			// the tree to a valid location.
			// Requires: iter.node is non-null.
			template <typename IterType>
			static IterType internal_last(IterType iter);

			// Returns an iterator pointing to the leaf position at which key would
			// reside in the tree. We provide 2 versions of internal_locate. The first
			// version uses a less-than comparator and is incapable of distinguishing when
			// there is an exact match. The second version is for the key-compare-to
			// specialization and distinguishes exact matches. The key-compare-to
			// specialization allows the caller to avoid a subsequent comparison to
			// determine if an exact match was made, which is important for keys with
			// expensive comparison, such as strings.
			template <typename K>
			SearchResult<iterator, is_key_compare_to::value> internal_locate(
			    const K &key) const;

			template <typename K>
			SearchResult<iterator, false> internal_locate_impl(
			    const K &key, std::false_type /* IsCompareTo */) const;

			template <typename K>
			SearchResult<iterator, true> internal_locate_impl(
			    const K &key, std::true_type /* IsCompareTo */) const;

			// Internal routine which implements lower_bound().
			template <typename K>
			iterator internal_lower_bound(const K &key) const;

			// Internal routine which implements upper_bound().
			template <typename K>
			iterator internal_upper_bound(const K &key) const;

			// Internal routine which implements find().
			template <typename K>
			iterator internal_find(const K &key) const;

			// Deletes a node and all of its children.
			void internal_clear(node_type *node);

			// Verifies the tree structure of node.
			size_type internal_verify(const node_type *node,
			                          const key_type *lo, const key_type *hi) const;

			node_stats internal_stats(const node_type *node) const
			{
				// The root can be a static empty node.
				if (node == nullptr || (node == root() && empty())) {
					return node_stats(0, 0);
				}
				if (node->leaf()) {
					return node_stats(1, 0);
				}
				node_stats res(0, 1);
				for (int i = 0; i <= node->count(); ++i) {
					res += internal_stats(node->child(i));
				}
				return res;
			}

		public:
			// Exposed only for tests.
			static bool testonly_uses_linear_node_search()
			{
				return node_type::testonly_uses_linear_node_search();
			}

		private:
			// We use compressed tuple in order to save space because key_compare and
			// allocator_type are usually empty.
			phmap::priv::CompressedTuple<key_compare, allocator_type,
			      node_type *>
			      root_;

			// A pointer to the rightmost node. Note that the leftmost node is stored as
			// the root's parent.
			node_type *rightmost_;

			// Number of values.
			size_type size_;
		};

////
// btree_node methods
		template <typename P>
		template <typename... Args>
		inline void btree_node<P>::emplace_value(const size_type i,
		        allocator_type *alloc,
		        Args &&... args)
		{
			assert(i <= count());
			// Shift old values to create space for new value and then construct it in
			// place.
			if (i < count()) {
				value_init(count(), alloc, slot(count() - 1));
				for (size_type j = count() - 1; j > i; --j)
					params_type::move(alloc, slot(j - 1), slot(j));
				value_destroy(i, alloc);
			}
			value_init(i, alloc, std::forward<Args>(args)...);
			set_count((field_type)(count() + 1));

			if (!leaf() && count() > i + 1) {
				for (int j = count(); j > (int)(i + 1); --j) {
					set_child(j, child(j - 1));
				}
				clear_child(i + 1);
			}
		}

		template <typename P>
		inline void btree_node<P>::remove_value(const int i, allocator_type *alloc)
		{
			if (!leaf() && count() > i + 1) {
				assert(child(i + 1)->count() == 0);
				for (size_type j = i + 1; j < count(); ++j) {
					set_child(j, child(j + 1));
				}
				clear_child(count());
			}

			remove_values_ignore_children(i, /*to_erase=*/1, alloc);
		}

		template <typename P>
		inline void btree_node<P>::remove_values_ignore_children(
		    int i, size_type to_erase, allocator_type *alloc)
		{
			params_type::move(alloc, slot(i + to_erase), slot(count()), slot(i));
			value_destroy_n(count() - to_erase, to_erase, alloc);
			set_count((field_type)(count() - to_erase));
		}

		template <typename P>
		void btree_node<P>::rebalance_right_to_left(const int to_move,
		        btree_node *right,
		        allocator_type *alloc)
		{
			assert(parent() == right->parent());
			assert(position() + 1 == right->position());
			assert(right->count() >= count());
			assert(to_move >= 1);
			assert(to_move <= right->count());

			// 1) Move the delimiting value in the parent to the left node.
			value_init(count(), alloc, parent()->slot(position()));

			// 2) Move the (to_move - 1) values from the right node to the left node.
			right->uninitialized_move_n(to_move - 1, 0, count() + 1, this, alloc);

			// 3) Move the new delimiting value to the parent from the right node.
			params_type::move(alloc, right->slot(to_move - 1),
			                  parent()->slot(position()));

			// 4) Shift the values in the right node to their correct position.
			params_type::move(alloc, right->slot(to_move), right->slot(right->count()),
			                  right->slot(0));

			// 5) Destroy the now-empty to_move entries in the right node.
			right->value_destroy_n(right->count() - to_move, to_move, alloc);

			if (!leaf()) {
				// Move the child pointers from the right to the left node.
				for (int i = 0; i < to_move; ++i) {
					init_child(count() + i + 1, right->child(i));
				}
				for (int i = 0; i <= right->count() - to_move; ++i) {
					assert(i + to_move <= right->max_count());
					right->init_child(i, right->child(i + to_move));
					right->clear_child(i + to_move);
				}
			}

			// Fixup the counts on the left and right nodes.
			set_count((field_type)(count() + to_move));
			right->set_count((field_type)(right->count() - to_move));
		}

		template <typename P>
		void btree_node<P>::rebalance_left_to_right(const int to_move,
		        btree_node *right,
		        allocator_type *alloc)
		{
			assert(parent() == right->parent());
			assert(position() + 1 == right->position());
			assert(count() >= right->count());
			assert(to_move >= 1);
			assert(to_move <= count());

			// Values in the right node are shifted to the right to make room for the
			// new to_move values. Then, the delimiting value in the parent and the
			// other (to_move - 1) values in the left node are moved into the right node.
			// Lastly, a new delimiting value is moved from the left node into the
			// parent, and the remaining empty left node entries are destroyed.

			if (right->count() >= to_move) {
				// The original location of the right->count() values are sufficient to hold
				// the new to_move entries from the parent and left node.

				// 1) Shift existing values in the right node to their correct positions.
				right->uninitialized_move_n(to_move, right->count() - to_move,
				                            right->count(), right, alloc);
				if (right->count() > to_move) {
					for (slot_type *src = right->slot(right->count() - to_move - 1),
					        *dest = right->slot(right->count() - 1),
					        *end = right->slot(0);
					        src >= end; --src, --dest) {
						params_type::move(alloc, src, dest);
					}
				}

				// 2) Move the delimiting value in the parent to the right node.
				params_type::move(alloc, parent()->slot(position()),
				                  right->slot(to_move - 1));

				// 3) Move the (to_move - 1) values from the left node to the right node.
				params_type::move(alloc, slot(count() - (to_move - 1)), slot(count()),
				                  right->slot(0));
			}
			else {
				// The right node does not have enough initialized space to hold the new
				// to_move entries, so part of them will move to uninitialized space.

				// 1) Shift existing values in the right node to their correct positions.
				right->uninitialized_move_n(right->count(), 0, to_move, right, alloc);

				// 2) Move the delimiting value in the parent to the right node.
				right->value_init(to_move - 1, alloc, parent()->slot(position()));

				// 3) Move the (to_move - 1) values from the left node to the right node.
				const size_type uninitialized_remaining = to_move - right->count() - 1;
				uninitialized_move_n(uninitialized_remaining,
				                     count() - uninitialized_remaining, right->count(),
				                     right, alloc);
				params_type::move(alloc, slot(count() - (to_move - 1)),
				                  slot(count() - uninitialized_remaining), right->slot(0));
			}

			// 4) Move the new delimiting value to the parent from the left node.
			params_type::move(alloc, slot(count() - to_move), parent()->slot(position()));

			// 5) Destroy the now-empty to_move entries in the left node.
			value_destroy_n(count() - to_move, to_move, alloc);

			if (!leaf()) {
				// Move the child pointers from the left to the right node.
				for (int i = right->count(); i >= 0; --i) {
					right->init_child(i + to_move, right->child(i));
					right->clear_child(i);
				}
				for (int i = 1; i <= to_move; ++i) {
					right->init_child(i - 1, child(count() - to_move + i));
					clear_child(count() - to_move + i);
				}
			}

			// Fixup the counts on the left and right nodes.
			set_count((field_type)(count() - to_move));
			right->set_count((field_type)(right->count() + to_move));
		}

		template <typename P>
		void btree_node<P>::split(const int insert_position, btree_node *dest,
		                          allocator_type *alloc)
		{
			assert(dest->count() == 0);
			assert(max_count() == kNodeValues);

			// We bias the split based on the position being inserted. If we're
			// inserting at the beginning of the left node then bias the split to put
			// more values on the right node. If we're inserting at the end of the
			// right node then bias the split to put more values on the left node.
			if (insert_position == 0) {
				dest->set_count((field_type)(count() - 1));
			}
			else if (insert_position == kNodeValues) {
				dest->set_count(0);
			}
			else {
				dest->set_count((field_type)(count() / 2));
			}
			set_count((field_type)(count() - dest->count()));
			assert(count() >= 1);

			// Move values from the left sibling to the right sibling.
			uninitialized_move_n(dest->count(), count(), 0, dest, alloc);

			// Destroy the now-empty entries in the left node.
			value_destroy_n(count(), dest->count(), alloc);

			// The split key is the largest value in the left sibling.
			set_count((field_type)(count() - 1));
			parent()->emplace_value(position(), alloc, slot(count()));
			value_destroy(count(), alloc);
			parent()->init_child(position() + 1, dest);

			if (!leaf()) {
				for (int i = 0; i <= dest->count(); ++i) {
					assert(child(count() + i + 1) != nullptr);
					dest->init_child(i, child(count() + i + 1));
					clear_child(count() + i + 1);
				}
			}
		}

		template <typename P>
		void btree_node<P>::merge(btree_node *src, allocator_type *alloc)
		{
			assert(parent() == src->parent());
			assert(position() + 1 == src->position());

			// Move the delimiting value to the left node.
			value_init(count(), alloc, parent()->slot(position()));

			// Move the values from the right to the left node.
			src->uninitialized_move_n(src->count(), 0, count() + 1, this, alloc);

			// Destroy the now-empty entries in the right node.
			src->value_destroy_n(0, src->count(), alloc);

			if (!leaf()) {
				// Move the child pointers from the right to the left node.
				for (int i = 0; i <= src->count(); ++i) {
					init_child(count() + i + 1, src->child(i));
					src->clear_child(i);
				}
			}

			// Fixup the counts on the src and dest nodes.
			set_count((field_type)(1 + count() + src->count()));
			src->set_count(0);

			// Remove the value on the parent node.
			parent()->remove_value(position(), alloc);
		}

		template <typename P>
		void btree_node<P>::swap(btree_node *x, allocator_type *alloc)
		{
			using std::swap;
			assert(leaf() == x->leaf());

			// Determine which is the smaller/larger node.
			btree_node *smaller = this, *larger = x;
			if (smaller->count() > larger->count()) {
				swap(smaller, larger);
			}

			// Swap the values.
			for (slot_type *a = smaller->slot(0), *b = larger->slot(0),
			        *end = a + smaller->count();
			        a != end; ++a, ++b) {
				params_type::swap(alloc, a, b);
			}

			// Move values that can't be swapped.
			const size_type to_move = larger->count() - smaller->count();
			larger->uninitialized_move_n(to_move, smaller->count(), smaller->count(),
			                             smaller, alloc);
			larger->value_destroy_n(smaller->count(), to_move, alloc);

			if (!leaf()) {
				// Swap the child pointers.
				std::swap_ranges(&smaller->mutable_child(0),
				                 &smaller->mutable_child(smaller->count() + 1),
				                 &larger->mutable_child(0));
				// Update swapped children's parent pointers.
				int i = 0;
				for (; i <= smaller->count(); ++i) {
					smaller->child(i)->set_parent(smaller);
					larger->child(i)->set_parent(larger);
				}
				// Move the child pointers that couldn't be swapped.
				for (; i <= larger->count(); ++i) {
					smaller->init_child(i, larger->child(i));
					larger->clear_child(i);
				}
			}

			// Swap the counts.
			swap(mutable_count(), x->mutable_count());
		}

////
// btree_iterator methods
		template <typename N, typename R, typename P>
		void btree_iterator<N, R, P>::increment_slow()
		{
			if (node->leaf()) {
				assert(position >= node->count());
				btree_iterator save(*this);
				while (position == node->count() && !node->is_root()) {
					assert(node->parent()->child(node->position()) == node);
					position = node->position();
					node = node->parent();
				}
				if (position == node->count()) {
					*this = save;
				}
			}
			else {
				assert(position < node->count());
				node = node->child(position + 1);
				while (!node->leaf()) {
					node = node->child(0);
				}
				position = 0;
			}
		}

		template <typename N, typename R, typename P>
		void btree_iterator<N, R, P>::decrement_slow()
		{
			if (node->leaf()) {
				assert(position <= -1);
				btree_iterator save(*this);
				while (position < 0 && !node->is_root()) {
					assert(node->parent()->child(node->position()) == node);
					position = node->position() - 1;
					node = node->parent();
				}
				if (position < 0) {
					*this = save;
				}
			}
			else {
				assert(position >= 0);
				node = node->child(position);
				while (!node->leaf()) {
					node = node->child(node->count());
				}
				position = node->count() - 1;
			}
		}

////
// btree methods
		template <typename P>
		template <typename Btree>
		void btree<P>::copy_or_move_values_in_order(Btree *x)
		{
			static_assert(std::is_same<btree, Btree>::value ||
			              std::is_same<const btree, Btree>::value,
			              "Btree type must be same or const.");
			assert(empty());

			// We can avoid key comparisons because we know the order of the
			// values is the same order we'll store them in.
			auto iter = x->begin();
			if (iter == x->end()) return;
			insert_multi(maybe_move_from_iterator(iter));
			++iter;
			for (; iter != x->end(); ++iter) {
				// If the btree is not empty, we can just insert the new value at the end
				// of the tree.
				internal_emplace(end(), maybe_move_from_iterator(iter));
			}
		}

		template <typename P>
		constexpr bool btree<P>::static_assert_validation()
		{
			static_assert(std::is_nothrow_copy_constructible<key_compare>::value,
			              "Key comparison must be nothrow copy constructible");
			static_assert(std::is_nothrow_copy_constructible<allocator_type>::value,
			              "Allocator must be nothrow copy constructible");
			static_assert(type_traits_internal::is_trivially_copyable<iterator>::value,
			              "iterator not trivially copyable.");

			// Note: We assert that kTargetValues, which is computed from
			// Params::kTargetNodeSize, must fit the node_type::field_type.
			static_assert(
			    kNodeValues < (1 << (8 * sizeof(typename node_type::field_type))),
			    "target node size too large");

			// Verify that key_compare returns an phmap::{weak,strong}_ordering or bool.
			using compare_result_type =
			    phmap::invoke_result_t<key_compare, key_type, key_type>;
			static_assert(
			    std::is_same<compare_result_type, bool>::value ||
			    std::is_convertible<compare_result_type, phmap::weak_ordering>::value,
			    "key comparison function must return phmap::{weak,strong}_ordering or "
			    "bool.");

			// Test the assumption made in setting kNodeSlotSpace.
			static_assert(node_type::MinimumOverhead() >= sizeof(void *) + 4,
			              "node space assumption incorrect");

			return true;
		}

		template <typename P>
		btree<P>::btree(const key_compare &comp, const allocator_type &alloc)
			: root_(comp, alloc, EmptyNode()), rightmost_(EmptyNode()), size_(0) {}

		template <typename P>
		btree<P>::btree(const btree &x) : btree(x.key_comp(), x.allocator())
		{
			copy_or_move_values_in_order(&x);
		}

		template <typename P>
		template <typename... Args>
		auto btree<P>::insert_unique(const key_type &key, Args &&... args)
		-> std::pair<iterator, bool>
		{
			if (empty()) {
				mutable_root() = rightmost_ = new_leaf_root_node(1);
			}

			auto res = internal_locate(key);
			iterator &iter = res.value;

			if (res.HasMatch()) {
				if (res.IsEq()) {
					// The key already exists in the tree, do nothing.
					return {iter, false};
				}
			}
			else {
				iterator last = internal_last(iter);
				if (last.node && !compare_keys(key, last.key())) {
					// The key already exists in the tree, do nothing.
					return {last, false};
				}
			}
			return {internal_emplace(iter, std::forward<Args>(args)...), true};
		}

		template <typename P>
		template <typename... Args>
		inline auto btree<P>::insert_hint_unique(iterator position, const key_type &key,
		        Args &&... args)
		-> std::pair<iterator, bool>
		{
			if (!empty()) {
				if (position == end() || compare_keys(key, position.key())) {
					iterator prev = position;
					if (position == begin() || compare_keys((--prev).key(), key)) {
						// prev.key() < key < position.key()
						return {internal_emplace(position, std::forward<Args>(args)...), true};
					}
				}
				else if (compare_keys(position.key(), key)) {
					++position;
					if (position == end() || compare_keys(key, position.key())) {
						// {original `position`}.key() < key < {current `position`}.key()
						return {internal_emplace(position, std::forward<Args>(args)...), true};
					}
				}
				else {
					// position.key() == key
					return {position, false};
				}
			}
			return insert_unique(key, std::forward<Args>(args)...);
		}

		template <typename P>
		template <typename InputIterator>
		void btree<P>::insert_iterator_unique(InputIterator b, InputIterator e)
		{
			for (; b != e; ++b) {
				insert_hint_unique(end(), params_type::key(*b), *b);
			}
		}

		template <typename P>
		template <typename ValueType>
		auto btree<P>::insert_multi(const key_type &key, ValueType &&v) -> iterator
		{
			if (empty()) {
				mutable_root() = rightmost_ = new_leaf_root_node(1);
			}

			iterator iter = internal_upper_bound(key);
			if (iter.node == nullptr) {
				iter = end();
			}
			return internal_emplace(iter, std::forward<ValueType>(v));
		}

		template <typename P>
		template <typename ValueType>
		auto btree<P>::insert_hint_multi(iterator position, ValueType &&v) -> iterator
		{
			if (!empty()) {
				const key_type &key = params_type::key(v);
				if (position == end() || !compare_keys(position.key(), key)) {
					iterator prev = position;
					if (position == begin() || !compare_keys(key, (--prev).key())) {
						// prev.key() <= key <= position.key()
						return internal_emplace(position, std::forward<ValueType>(v));
					}
				}
				else {
					iterator next = position;
					++next;
					if (next == end() || !compare_keys(next.key(), key)) {
						// position.key() < key <= next.key()
						return internal_emplace(next, std::forward<ValueType>(v));
					}
				}
			}
			return insert_multi(std::forward<ValueType>(v));
		}

		template <typename P>
		template <typename InputIterator>
		void btree<P>::insert_iterator_multi(InputIterator b, InputIterator e)
		{
			for (; b != e; ++b) {
				insert_hint_multi(end(), *b);
			}
		}

		template <typename P>
		auto btree<P>::operator=(const btree &x) -> btree &
		{
			if (this != &x) {
				clear();

				*mutable_key_comp() = x.key_comp();
				if (phmap::allocator_traits<
				        allocator_type>::propagate_on_container_copy_assignment::value) {
					*mutable_allocator() = x.allocator();
				}

				copy_or_move_values_in_order(&x);
			}
			return *this;
		}

		template <typename P>
		auto btree<P>::operator=(btree &&x) noexcept -> btree &
		{
			if (this != &x) {
				clear();

				using std::swap;
				if (phmap::allocator_traits<
				        allocator_type>::propagate_on_container_copy_assignment::value) {
					// Note: `root_` also contains the allocator and the key comparator.
					swap(root_, x.root_);
					swap(rightmost_, x.rightmost_);
					swap(size_, x.size_);
				}
				else {
					if (allocator() == x.allocator()) {
						swap(mutable_root(), x.mutable_root());
						swap(*mutable_key_comp(), *x.mutable_key_comp());
						swap(rightmost_, x.rightmost_);
						swap(size_, x.size_);
					}
					else {
						// We aren't allowed to propagate the allocator and the allocator is
						// different so we can't take over its memory. We must move each element
						// individually. We need both `x` and `this` to have `x`s key comparator
						// while moving the values so we can't swap the key comparators.
						*mutable_key_comp() = x.key_comp();
						copy_or_move_values_in_order(&x);
					}
				}
			}
			return *this;
		}

		template <typename P>
		auto btree<P>::erase(iterator iter) -> iterator
		{
			bool internal_delete = false;
			if (!iter.node->leaf()) {
				// Deletion of a value on an internal node. First, move the largest value
				// from our left child here, then delete that position (in remove_value()
				// below). We can get to the largest value from our left child by
				// decrementing iter.
				iterator internal_iter(iter);
				--iter;
				assert(iter.node->leaf());
				params_type::move(mutable_allocator(), iter.node->slot(iter.position),
				                  internal_iter.node->slot(internal_iter.position));
				internal_delete = true;
			}

			// Delete the key from the leaf.
			iter.node->remove_value(iter.position, mutable_allocator());
			--size_;

			// We want to return the next value after the one we just erased. If we
			// erased from an internal node (internal_delete == true), then the next
			// value is ++(++iter). If we erased from a leaf node (internal_delete ==
			// false) then the next value is ++iter. Note that ++iter may point to an
			// internal node and the value in the internal node may move to a leaf node
			// (iter.node) when rebalancing is performed at the leaf level.

			iterator res = rebalance_after_delete(iter);

			// If we erased from an internal node, advance the iterator.
			if (internal_delete) {
				++res;
			}
			return res;
		}

		template <typename P>
		auto btree<P>::rebalance_after_delete(iterator iter) -> iterator
		{
			// Merge/rebalance as we walk back up the tree.
			iterator res(iter);
			bool first_iteration = true;
			for (;;) {
				if (iter.node == root()) {
					try_shrink();
					if (empty()) {
						return end();
					}
					break;
				}
				if (iter.node->count() >= kMinNodeValues) {
					break;
				}
				bool merged = try_merge_or_rebalance(&iter);
				// On the first iteration, we should update `res` with `iter` because `res`
				// may have been invalidated.
				if (first_iteration) {
					res = iter;
					first_iteration = false;
				}
				if (!merged) {
					break;
				}
				iter.position = iter.node->position();
				iter.node = iter.node->parent();
			}

			// Adjust our return value. If we're pointing at the end of a node, advance
			// the iterator.
			if (res.position == res.node->count()) {
				res.position = res.node->count() - 1;
				++res;
			}

			return res;
		}

		template <typename P>
		auto btree<P>::erase(iterator _begin, iterator _end)
		-> std::pair<size_type, iterator>
		{
			difference_type count = std::distance(_begin, _end);
			assert(count >= 0);

			if (count == 0) {
				return {0, _begin};
			}

			if (count == (difference_type)size_) {
				clear();
				return {count, this->end()};
			}

			if (_begin.node == _end.node) {
				erase_same_node(_begin, _end);
				size_ -= count;
				return {count, rebalance_after_delete(_begin)};
			}

			const size_type target_size = size_ - count;
			while (size_ > target_size) {
				if (_begin.node->leaf()) {
					const size_type remaining_to_erase = size_ - target_size;
					const size_type remaining_in_node = _begin.node->count() - _begin.position;
					_begin = erase_from_leaf_node(
					             _begin, (std::min)(remaining_to_erase, remaining_in_node));
				}
				else {
					_begin = erase(_begin);
				}
			}
			return {count, _begin};
		}

		template <typename P>
		void btree<P>::erase_same_node(iterator _begin, iterator _end)
		{
			assert(_begin.node == _end.node);
			assert(_end.position > _begin.position);

			node_type *node = _begin.node;
			size_type to_erase = _end.position - _begin.position;
			if (!node->leaf()) {
				// Delete all children between _begin and _end.
				for (size_type i = 0; i < to_erase; ++i) {
					internal_clear(node->child(_begin.position + i + 1));
				}
				// Rotate children after _end into new positions.
				for (size_type i = _begin.position + to_erase + 1; i <= node->count(); ++i) {
					node->set_child(i - to_erase, node->child(i));
					node->clear_child(i);
				}
			}
			node->remove_values_ignore_children(_begin.position, to_erase,
			                                    mutable_allocator());

			// Do not need to update rightmost_, because
			// * either _end == this->end(), and therefore node == rightmost_, and still
			//   exists
			// * or _end != this->end(), and therefore rightmost_ hasn't been erased, since
			//   it wasn't covered in [_begin, _end)
		}

		template <typename P>
		auto btree<P>::erase_from_leaf_node(iterator _begin, size_type to_erase)
		-> iterator
		{
			node_type *node = _begin.node;
			assert(node->leaf());
			assert(node->count() > _begin.position);
			assert(_begin.position + to_erase <= node->count());

			node->remove_values_ignore_children(_begin.position, to_erase,
			                                    mutable_allocator());

			size_ -= to_erase;

			return rebalance_after_delete(_begin);
		}

		template <typename P>
		template <typename K>
		auto btree<P>::erase_unique(const K &key) -> size_type
		{
			const iterator iter = internal_find(key);
			if (iter.node == nullptr) {
				// The key doesn't exist in the tree, return nothing done.
				return 0;
			}
			erase(iter);
			return 1;
		}

		template <typename P>
		template <typename K>
		auto btree<P>::erase_multi(const K &key) -> size_type
		{
			const iterator _begin = internal_lower_bound(key);
			if (_begin.node == nullptr) {
				// The key doesn't exist in the tree, return nothing done.
				return 0;
			}
			// Delete all of the keys between _begin and upper_bound(key).
			const iterator _end = internal_end(internal_upper_bound(key));
			return erase(_begin, _end).first;
		}

		template <typename P>
		void btree<P>::clear()
		{
			if (!empty()) {
				internal_clear(root());
			}
			mutable_root() = EmptyNode();
			rightmost_ = EmptyNode();
			size_ = 0;
		}

		template <typename P>
		void btree<P>::swap(btree &x)
		{
			using std::swap;
			if (phmap::allocator_traits<
			        allocator_type>::propagate_on_container_swap::value) {
				// Note: `root_` also contains the allocator and the key comparator.
				swap(root_, x.root_);
			}
			else {
				// It's undefined behavior if the allocators are unequal here.
				assert(allocator() == x.allocator());
				swap(mutable_root(), x.mutable_root());
				swap(*mutable_key_comp(), *x.mutable_key_comp());
			}
			swap(rightmost_, x.rightmost_);
			swap(size_, x.size_);
		}

		template <typename P>
		void btree<P>::verify() const
		{
			assert(root() != nullptr);
			assert(leftmost() != nullptr);
			assert(rightmost_ != nullptr);
			assert(empty() || size() == internal_verify(root(), nullptr, nullptr));
			assert(leftmost() == (++const_iterator(root(), -1)).node);
			assert(rightmost_ == (--const_iterator(root(), root()->count())).node);
			assert(leftmost()->leaf());
			assert(rightmost_->leaf());
		}

		template <typename P>
		void btree<P>::rebalance_or_split(iterator *iter)
		{
			node_type *&node = iter->node;
			int &insert_position = iter->position;
			assert(node->count() == node->max_count());
			assert(kNodeValues == node->max_count());

			// First try to make room on the node by rebalancing.
			node_type *parent = node->parent();
			if (node != root()) {
				if (node->position() > 0) {
					// Try rebalancing with our left sibling.
					node_type *left = parent->child(node->position() - 1);
					assert(left->max_count() == kNodeValues);
					if (left->count() < kNodeValues) {
						// We bias rebalancing based on the position being inserted. If we're
						// inserting at the end of the right node then we bias rebalancing to
						// fill up the left node.
						int to_move = (kNodeValues - left->count()) /
						              (1 + (insert_position < kNodeValues));
						to_move = (std::max)(1, to_move);

						if (((insert_position - to_move) >= 0) ||
						        ((left->count() + to_move) < kNodeValues)) {
							left->rebalance_right_to_left(to_move, node, mutable_allocator());

							assert(node->max_count() - node->count() == to_move);
							insert_position = insert_position - to_move;
							if (insert_position < 0) {
								insert_position = insert_position + left->count() + 1;
								node = left;
							}

							assert(node->count() < node->max_count());
							return;
						}
					}
				}

				if (node->position() < parent->count()) {
					// Try rebalancing with our right sibling.
					node_type *right = parent->child(node->position() + 1);
					assert(right->max_count() == kNodeValues);
					if (right->count() < kNodeValues) {
						// We bias rebalancing based on the position being inserted. If we're
						// inserting at the _beginning of the left node then we bias rebalancing
						// to fill up the right node.
						int to_move =
						    (kNodeValues - right->count()) / (1 + (insert_position > 0));
						to_move = (std::max)(1, to_move);

						if ((insert_position <= (node->count() - to_move)) ||
						        ((right->count() + to_move) < kNodeValues)) {
							node->rebalance_left_to_right(to_move, right, mutable_allocator());

							if (insert_position > node->count()) {
								insert_position = insert_position - node->count() - 1;
								node = right;
							}

							assert(node->count() < node->max_count());
							return;
						}
					}
				}

				// Rebalancing failed, make sure there is room on the parent node for a new
				// value.
				assert(parent->max_count() == kNodeValues);
				if (parent->count() == kNodeValues) {
					iterator parent_iter(node->parent(), node->position());
					rebalance_or_split(&parent_iter);
				}
			}
			else {
				// Rebalancing not possible because this is the root node.
				// Create a new root node and set the current root node as the child of the
				// new root.
				parent = new_internal_node(parent);
				parent->init_child(0, root());
				mutable_root() = parent;
				// If the former root was a leaf node, then it's now the rightmost node.
				assert(!parent->child(0)->leaf() || parent->child(0) == rightmost_);
			}

			// Split the node.
			node_type *split_node;
			if (node->leaf()) {
				split_node = new_leaf_node(parent);
				node->split(insert_position, split_node, mutable_allocator());
				if (rightmost_ == node) rightmost_ = split_node;
			}
			else {
				split_node = new_internal_node(parent);
				node->split(insert_position, split_node, mutable_allocator());
			}

			if (insert_position > node->count()) {
				insert_position = insert_position - node->count() - 1;
				node = split_node;
			}
		}

		template <typename P>
		void btree<P>::merge_nodes(node_type *left, node_type *right)
		{
			left->merge(right, mutable_allocator());
			if (right->leaf()) {
				if (rightmost_ == right) rightmost_ = left;
				delete_leaf_node(right);
			}
			else {
				delete_internal_node(right);
			}
		}

		template <typename P>
		bool btree<P>::try_merge_or_rebalance(iterator *iter)
		{
			node_type *parent = iter->node->parent();
			if (iter->node->position() > 0) {
				// Try merging with our left sibling.
				node_type *left = parent->child(iter->node->position() - 1);
				assert(left->max_count() == kNodeValues);
				if ((1 + left->count() + iter->node->count()) <= kNodeValues) {
					iter->position += 1 + left->count();
					merge_nodes(left, iter->node);
					iter->node = left;
					return true;
				}
			}
			if (iter->node->position() < parent->count()) {
				// Try merging with our right sibling.
				node_type *right = parent->child(iter->node->position() + 1);
				assert(right->max_count() == kNodeValues);
				if ((1 + iter->node->count() + right->count()) <= kNodeValues) {
					merge_nodes(iter->node, right);
					return true;
				}
				// Try rebalancing with our right sibling. We don't perform rebalancing if
				// we deleted the first element from iter->node and the node is not
				// empty. This is a small optimization for the common pattern of deleting
				// from the front of the tree.
				if ((right->count() > kMinNodeValues) &&
				        ((iter->node->count() == 0) ||
				         (iter->position > 0))) {
					int to_move = (right->count() - iter->node->count()) / 2;
					to_move = (std::min)(to_move, right->count() - 1);
					iter->node->rebalance_right_to_left(to_move, right, mutable_allocator());
					return false;
				}
			}
			if (iter->node->position() > 0) {
				// Try rebalancing with our left sibling. We don't perform rebalancing if
				// we deleted the last element from iter->node and the node is not
				// empty. This is a small optimization for the common pattern of deleting
				// from the back of the tree.
				node_type *left = parent->child(iter->node->position() - 1);
				if ((left->count() > kMinNodeValues) &&
				        ((iter->node->count() == 0) ||
				         (iter->position < iter->node->count()))) {
					int to_move = (left->count() - iter->node->count()) / 2;
					to_move = (std::min)(to_move, left->count() - 1);
					left->rebalance_left_to_right(to_move, iter->node, mutable_allocator());
					iter->position += to_move;
					return false;
				}
			}
			return false;
		}

		template <typename P>
		void btree<P>::try_shrink()
		{
			if (root()->count() > 0) {
				return;
			}
			// Deleted the last item on the root node, shrink the height of the tree.
			if (root()->leaf()) {
				assert(size() == 0);
				delete_leaf_node(root());
				mutable_root() = EmptyNode();
				rightmost_ = EmptyNode();
			}
			else {
				node_type *child = root()->child(0);
				child->make_root();
				delete_internal_node(root());
				mutable_root() = child;
			}
		}

		template <typename P>
		template <typename IterType>
		inline IterType btree<P>::internal_last(IterType iter)
		{
			assert(iter.node != nullptr);
			while (iter.position == iter.node->count()) {
				iter.position = iter.node->position();
				iter.node = iter.node->parent();
				if (iter.node->leaf()) {
					iter.node = nullptr;
					break;
				}
			}
			return iter;
		}

		template <typename P>
		template <typename... Args>
		inline auto btree<P>::internal_emplace(iterator iter, Args &&... args)
		-> iterator
		{
			if (!iter.node->leaf()) {
				// We can't insert on an internal node. Instead, we'll insert after the
				// previous value which is guaranteed to be on a leaf node.
				--iter;
				++iter.position;
			}
			const int max_count = iter.node->max_count();
			if (iter.node->count() == max_count) {
				// Make room in the leaf for the new item.
				if (max_count < kNodeValues) {
					// Insertion into the root where the root is smaller than the full node
					// size. Simply grow the size of the root node.
					assert(iter.node == root());
					iter.node =
					    new_leaf_root_node((std::min<int>)(kNodeValues, 2 * max_count));
					iter.node->swap(root(), mutable_allocator());
					delete_leaf_node(root());
					mutable_root() = iter.node;
					rightmost_ = iter.node;
				}
				else {
					rebalance_or_split(&iter);
				}
			}
			iter.node->emplace_value(iter.position, mutable_allocator(),
			                         std::forward<Args>(args)...);
			++size_;
			return iter;
		}

		template <typename P>
		template <typename K>
		inline auto btree<P>::internal_locate(const K &key) const
		-> SearchResult<iterator, is_key_compare_to::value>
		{
			return internal_locate_impl(key, is_key_compare_to());
		}

		template <typename P>
		template <typename K>
		inline auto btree<P>::internal_locate_impl(
		    const K &key, std::false_type /* IsCompareTo */) const
		-> SearchResult<iterator, false>
		{
			iterator iter(const_cast<node_type *>(root()), 0);
			for (;;) {
				iter.position = iter.node->lower_bound(key, key_comp()).value;
				// NOTE: we don't need to walk all the way down the tree if the keys are
				// equal, but determining equality would require doing an extra comparison
				// on each node on the way down, and we will need to go all the way to the
				// leaf node in the expected case.
				if (iter.node->leaf()) {
					break;
				}
				iter.node = iter.node->child(iter.position);
			}
			return {iter};
		}

		template <typename P>
		template <typename K>
		inline auto btree<P>::internal_locate_impl(
		    const K &key, std::true_type /* IsCompareTo */) const
		-> SearchResult<iterator, true>
		{
			iterator iter(const_cast<node_type *>(root()), 0);
			for (;;) {
				SearchResult<int, true> res = iter.node->lower_bound(key, key_comp());
				iter.position = res.value;
				if (res.match == MatchKind::kEq) {
					return {iter, MatchKind::kEq};
				}
				if (iter.node->leaf()) {
					break;
				}
				iter.node = iter.node->child(iter.position);
			}
			return {iter, MatchKind::kNe};
		}

		template <typename P>
		template <typename K>
		auto btree<P>::internal_lower_bound(const K &key) const -> iterator
		{
			iterator iter(const_cast<node_type *>(root()), 0);
			for (;;) {
				iter.position = iter.node->lower_bound(key, key_comp()).value;
				if (iter.node->leaf()) {
					break;
				}
				iter.node = iter.node->child(iter.position);
			}
			return internal_last(iter);
		}

		template <typename P>
		template <typename K>
		auto btree<P>::internal_upper_bound(const K &key) const -> iterator
		{
			iterator iter(const_cast<node_type *>(root()), 0);
			for (;;) {
				iter.position = iter.node->upper_bound(key, key_comp());
				if (iter.node->leaf()) {
					break;
				}
				iter.node = iter.node->child(iter.position);
			}
			return internal_last(iter);
		}

		template <typename P>
		template <typename K>
		auto btree<P>::internal_find(const K &key) const -> iterator
		{
			auto res = internal_locate(key);
			if (res.HasMatch()) {
				if (res.IsEq()) {
					return res.value;
				}
			}
			else {
				const iterator iter = internal_last(res.value);
				if (iter.node != nullptr && !compare_keys(key, iter.key())) {
					return iter;
				}
			}
			return {nullptr, 0};
		}

		template <typename P>
		void btree<P>::internal_clear(node_type *node)
		{
			if (!node->leaf()) {
				for (int i = 0; i <= node->count(); ++i) {
					internal_clear(node->child(i));
				}
				delete_internal_node(node);
			}
			else {
				delete_leaf_node(node);
			}
		}

		template <typename P>
		typename btree<P>::size_type btree<P>::internal_verify(
		    const node_type *node, const key_type *lo, const key_type *hi) const
		{
			assert(node->count() > 0);
			assert(node->count() <= node->max_count());
			if (lo) {
				assert(!compare_keys(node->key(0), *lo));
			}
			if (hi) {
				assert(!compare_keys(*hi, node->key(node->count() - 1)));
			}
			for (int i = 1; i < node->count(); ++i) {
				assert(!compare_keys(node->key(i), node->key(i - 1)));
			}
			size_type count = node->count();
			if (!node->leaf()) {
				for (int i = 0; i <= node->count(); ++i) {
					assert(node->child(i) != nullptr);
					assert(node->child(i)->parent() == node);
					assert(node->child(i)->position() == i);
					count += internal_verify(
					             node->child(i),
					             (i == 0) ? lo : &node->key(i - 1),
					             (i == node->count()) ? hi : &node->key(i));
				}
			}
			return count;
		}

// A common base class for btree_set, btree_map, btree_multiset, and btree_multimap.
// ---------------------------------------------------------------------------------
		template <typename Tree>
		class btree_container {
			using params_type = typename Tree::params_type;

		protected:
			// Alias used for heterogeneous lookup functions.
			// `key_arg<K>` evaluates to `K` when the functors are transparent and to
			// `key_type` otherwise. It permits template argument deduction on `K` for the
			// transparent case.
			template <class K>
			using key_arg =
			    typename KeyArg<IsTransparent<typename Tree::key_compare>::value>::
			    template type<K, typename Tree::key_type>;

		public:
			using key_type = typename Tree::key_type;
			using value_type = typename Tree::value_type;
			using size_type = typename Tree::size_type;
			using difference_type = typename Tree::difference_type;
			using key_compare = typename Tree::key_compare;
			using value_compare = typename Tree::value_compare;
			using allocator_type = typename Tree::allocator_type;
			using reference = typename Tree::reference;
			using const_reference = typename Tree::const_reference;
			using pointer = typename Tree::pointer;
			using const_pointer = typename Tree::const_pointer;
			using iterator = typename Tree::iterator;
			using const_iterator = typename Tree::const_iterator;
			using reverse_iterator = typename Tree::reverse_iterator;
			using const_reverse_iterator = typename Tree::const_reverse_iterator;
			using node_type = typename Tree::node_handle_type;

			// Constructors/assignments.
			btree_container() : tree_(key_compare(), allocator_type()) {}
			explicit btree_container(const key_compare &comp,
			                         const allocator_type &alloc = allocator_type())
				: tree_(comp, alloc) {}
			btree_container(const btree_container &x) = default;
			btree_container(btree_container &&x) noexcept = default;
			btree_container &operator=(const btree_container &x) = default;
			btree_container &operator=(btree_container &&x) noexcept(
			    std::is_nothrow_move_assignable<Tree>::value) = default;

			// Iterator routines.
			iterator begin()
			{
				return tree_.begin();
			}
			const_iterator begin() const
			{
				return tree_.begin();
			}
			const_iterator cbegin() const
			{
				return tree_.begin();
			}
			iterator end()
			{
				return tree_.end();
			}
			const_iterator end() const
			{
				return tree_.end();
			}
			const_iterator cend() const
			{
				return tree_.end();
			}
			reverse_iterator rbegin()
			{
				return tree_.rbegin();
			}
			const_reverse_iterator rbegin() const
			{
				return tree_.rbegin();
			}
			const_reverse_iterator crbegin() const
			{
				return tree_.rbegin();
			}
			reverse_iterator rend()
			{
				return tree_.rend();
			}
			const_reverse_iterator rend() const
			{
				return tree_.rend();
			}
			const_reverse_iterator crend() const
			{
				return tree_.rend();
			}

			// Lookup routines.
			// ----------------
			template <typename K = key_type>
			size_type count(const key_arg<K> &key) const
			{
				auto equal_range = this->equal_range(key);
				return std::distance(equal_range.first, equal_range.second);
			}
			template <typename K = key_type>
			iterator find(const key_arg<K> &key)
			{
				return tree_.find(key);
			}
			template <typename K = key_type>
			const_iterator find(const key_arg<K> &key) const
			{
				return tree_.find(key);
			}

			template <typename K = key_type>
			bool contains(const key_arg<K> &key) const
			{
				return find(key) != end();
			}

			template <typename K = key_type>
			iterator lower_bound(const key_arg<K> &key)
			{
				return tree_.lower_bound(key);
			}

			template <typename K = key_type>
			const_iterator lower_bound(const key_arg<K> &key) const
			{
				return tree_.lower_bound(key);
			}

			template <typename K = key_type>
			iterator upper_bound(const key_arg<K> &key)
			{
				return tree_.upper_bound(key);
			}

			template <typename K = key_type>
			const_iterator upper_bound(const key_arg<K> &key) const
			{
				return tree_.upper_bound(key);
			}

			template <typename K = key_type>
			std::pair<iterator, iterator> equal_range(const key_arg<K> &key)
			{
				return tree_.equal_range(key);
			}

			template <typename K = key_type>
			std::pair<const_iterator, const_iterator> equal_range(
			    const key_arg<K> &key) const
			{
				return tree_.equal_range(key);
			}

			iterator erase(const_iterator iter)
			{
				return tree_.erase(iterator(iter));
			}
			iterator erase(iterator iter)
			{
				return tree_.erase(iter);
			}
			iterator erase(const_iterator first, const_iterator last)
			{
				return tree_.erase(iterator(first), iterator(last)).second;
			}
			template <typename K = key_type>
			size_type erase(const key_arg<K> &key)
			{
				auto equal_range = this->equal_range(key);
				return tree_.erase_range(equal_range.first, equal_range.second).first;
			}
			node_type extract(iterator position)
			{
				// Use Move instead of Transfer, because the rebalancing code expects to
				// have a valid object to scribble metadata bits on top of.
				auto node = CommonAccess::Move<node_type>(get_allocator(), position.slot());
				erase(position);
				return node;
			}

			node_type extract(const_iterator position)
			{
				return extract(iterator(position));
			}

		public:
			void clear()
			{
				tree_.clear();
			}
			void swap(btree_container &x)
			{
				tree_.swap(x.tree_);
			}
			void verify() const
			{
				tree_.verify();
			}

			size_type size() const
			{
				return tree_.size();
			}
			size_type max_size() const
			{
				return tree_.max_size();
			}
			bool empty() const
			{
				return tree_.empty();
			}

			friend bool operator==(const btree_container &x, const btree_container &y)
			{
				if (x.size() != y.size()) return false;
				return std::equal(x.begin(), x.end(), y.begin());
			}

			friend bool operator!=(const btree_container &x, const btree_container &y)
			{
				return !(x == y);
			}

			friend bool operator<(const btree_container &x, const btree_container &y)
			{
				return std::lexicographical_compare(x.begin(), x.end(), y.begin(), y.end());
			}

			friend bool operator>(const btree_container &x, const btree_container &y)
			{
				return y < x;
			}

			friend bool operator<=(const btree_container &x, const btree_container &y)
			{
				return !(y < x);
			}

			friend bool operator>=(const btree_container &x, const btree_container &y)
			{
				return !(x < y);
			}

			// The allocator used by the btree.
			allocator_type get_allocator() const
			{
				return tree_.get_allocator();
			}

			// The key comparator used by the btree.
			key_compare key_comp() const
			{
				return tree_.key_comp();
			}
			value_compare value_comp() const
			{
				return tree_.value_comp();
			}

			// Support absl::Hash.
			template <typename State>
			friend State AbslHashValue(State h, const btree_container &b)
			{
				for (const auto &v : b) {
					h = State::combine(std::move(h), v);
				}
				return State::combine(std::move(h), b.size());
			}

		protected:
			Tree tree_;
		};

// A common base class for btree_set and btree_map.
// -----------------------------------------------
		template <typename Tree>
		class btree_set_container : public btree_container<Tree> {
			using super_type = btree_container<Tree>;
			using params_type = typename Tree::params_type;
			using init_type = typename params_type::init_type;
			using is_key_compare_to = typename params_type::is_key_compare_to;
			friend class BtreeNodePeer;

		protected:
			template <class K>
			using key_arg = typename super_type::template key_arg<K>;

		public:
			using key_type = typename Tree::key_type;
			using value_type = typename Tree::value_type;
			using size_type = typename Tree::size_type;
			using key_compare = typename Tree::key_compare;
			using allocator_type = typename Tree::allocator_type;
			using iterator = typename Tree::iterator;
			using const_iterator = typename Tree::const_iterator;
			using node_type = typename super_type::node_type;
			using insert_return_type = InsertReturnType<iterator, node_type>;
			using super_type::super_type;
			btree_set_container() {}

			template <class InputIterator>
			btree_set_container(InputIterator b, InputIterator e,
			                    const key_compare &comp = key_compare(),
			                    const allocator_type &alloc = allocator_type())
				: super_type(comp, alloc)
			{
				insert(b, e);
			}

			btree_set_container(std::initializer_list<init_type> init,
			                    const key_compare &comp = key_compare(),
			                    const allocator_type &alloc = allocator_type())
				: btree_set_container(init.begin(), init.end(), comp, alloc) {}

			btree_set_container(std::initializer_list<init_type> init,
			                    const allocator_type &alloc)
				: btree_set_container(init.begin(), init.end(), alloc) {}

			// Lookup routines.
			template <typename K = key_type>
			size_type count(const key_arg<K> &key) const
			{
				return this->tree_.count_unique(key);
			}

			// Insertion routines.
			std::pair<iterator, bool> insert(const value_type &x)
			{
				return this->tree_.insert_unique(params_type::key(x), x);
			}
			std::pair<iterator, bool> insert(value_type &&x)
			{
				return this->tree_.insert_unique(params_type::key(x), std::move(x));
			}
			template <typename... Args>
			std::pair<iterator, bool> emplace(Args &&... args)
			{
				init_type v(std::forward<Args>(args)...);
				return this->tree_.insert_unique(params_type::key(v), std::move(v));
			}
			iterator insert(const_iterator hint, const value_type &x)
			{
				return this->tree_
				       .insert_hint_unique(iterator(hint), params_type::key(x), x)
				       .first;
			}
			iterator insert(const_iterator hint, value_type &&x)
			{
				return this->tree_
				       .insert_hint_unique(iterator(hint), params_type::key(x),
				                           std::move(x))
				       .first;
			}

			template <typename... Args>
			iterator emplace_hint(const_iterator hint, Args &&... args)
			{
				init_type v(std::forward<Args>(args)...);
				return this->tree_
				       .insert_hint_unique(iterator(hint), params_type::key(v),
				                           std::move(v))
				       .first;
			}

			template <typename InputIterator>
			void insert(InputIterator b, InputIterator e)
			{
				this->tree_.insert_iterator_unique(b, e);
			}

			void insert(std::initializer_list<init_type> init)
			{
				this->tree_.insert_iterator_unique(init.begin(), init.end());
			}

			insert_return_type insert(node_type &&node)
			{
				if (!node) return {this->end(), false, node_type()};
				std::pair<iterator, bool> res =
				    this->tree_.insert_unique(params_type::key(CommonAccess::GetSlot(node)),
				                              CommonAccess::GetSlot(node));
				if (res.second) {
					CommonAccess::Destroy(&node);
					return {res.first, true, node_type()};
				}
				else {
					return {res.first, false, std::move(node)};
				}
			}

			iterator insert(const_iterator hint, node_type &&node)
			{
				if (!node) return this->end();
				std::pair<iterator, bool> res = this->tree_.insert_hint_unique(
				                                    iterator(hint), params_type::key(CommonAccess::GetSlot(node)),
				                                    CommonAccess::GetSlot(node));
				if (res.second) CommonAccess::Destroy(&node);
				return res.first;
			}

			template <typename K = key_type>
			size_type erase(const key_arg<K> &key)
			{
				return this->tree_.erase_unique(key);
			}
			using super_type::erase;

			template <typename K = key_type>
			node_type extract(const key_arg<K> &key)
			{
				auto it = this->find(key);
				return it == this->end() ? node_type() : extract(it);
			}

			using super_type::extract;

			// Merge routines.
			// Moves elements from `src` into `this`. If the element already exists in
			// `this`, it is left unmodified in `src`.
			template <
			    typename T,
			    typename phmap::enable_if_t<
			        phmap::conjunction<
			            std::is_same<value_type, typename T::value_type>,
			            std::is_same<allocator_type, typename T::allocator_type>,
			            std::is_same<typename params_type::is_map_container,
			                         typename T::params_type::is_map_container>>::value,
			        int> = 0>
			void merge(btree_container<T> &src)    // NOLINT
			{
				for (auto src_it = src.begin(); src_it != src.end();) {
					if (insert(std::move(*src_it)).second) {
						src_it = src.erase(src_it);
					}
					else {
						++src_it;
					}
				}
			}

			template <
			    typename T,
			    typename phmap::enable_if_t<
			        phmap::conjunction<
			            std::is_same<value_type, typename T::value_type>,
			            std::is_same<allocator_type, typename T::allocator_type>,
			            std::is_same<typename params_type::is_map_container,
			                         typename T::params_type::is_map_container>>::value,
			        int> = 0>
			void merge(btree_container<T> &&src)
			{
				merge(src);
			}
		};

// Base class for btree_map.
// -------------------------
		template <typename Tree>
		class btree_map_container : public btree_set_container<Tree> {
			using super_type = btree_set_container<Tree>;
			using params_type = typename Tree::params_type;

		protected:
			template <class K>
			using key_arg = typename super_type::template key_arg<K>;

		public:
			using key_type = typename Tree::key_type;
			using mapped_type = typename params_type::mapped_type;
			using value_type = typename Tree::value_type;
			using key_compare = typename Tree::key_compare;
			using allocator_type = typename Tree::allocator_type;
			using iterator = typename Tree::iterator;
			using const_iterator = typename Tree::const_iterator;

			// Inherit constructors.
			using super_type::super_type;
			btree_map_container() {}

			// Insertion routines.
			template <typename... Args>
			std::pair<iterator, bool> try_emplace(const key_type &k, Args &&... args)
			{
				return this->tree_.insert_unique(
				           k, std::piecewise_construct, std::forward_as_tuple(k),
				           std::forward_as_tuple(std::forward<Args>(args)...));
			}
			template <typename... Args>
			std::pair<iterator, bool> try_emplace(key_type &&k, Args &&... args)
			{
				// Note: `key_ref` exists to avoid a ClangTidy warning about moving from `k`
				// and then using `k` unsequenced. This is safe because the move is into a
				// forwarding reference and insert_unique guarantees that `key` is never
				// referenced after consuming `args`.
				const key_type& key_ref = k;
				return this->tree_.insert_unique(
				           key_ref, std::piecewise_construct, std::forward_as_tuple(std::move(k)),
				           std::forward_as_tuple(std::forward<Args>(args)...));
			}
			template <typename... Args>
			iterator try_emplace(const_iterator hint, const key_type &k,
			                     Args &&... args)
			{
				return this->tree_
				       .insert_hint_unique(iterator(hint), k, std::piecewise_construct,
				                           std::forward_as_tuple(k),
				                           std::forward_as_tuple(std::forward<Args>(args)...))
				       .first;
			}
			template <typename... Args>
			iterator try_emplace(const_iterator hint, key_type &&k, Args &&... args)
			{
				// Note: `key_ref` exists to avoid a ClangTidy warning about moving from `k`
				// and then using `k` unsequenced. This is safe because the move is into a
				// forwarding reference and insert_hint_unique guarantees that `key` is
				// never referenced after consuming `args`.
				const key_type& key_ref = k;
				return this->tree_
				       .insert_hint_unique(iterator(hint), key_ref, std::piecewise_construct,
				                           std::forward_as_tuple(std::move(k)),
				                           std::forward_as_tuple(std::forward<Args>(args)...))
				       .first;
			}
			mapped_type &operator[](const key_type &k)
			{
				return try_emplace(k).first->second;
			}
			mapped_type &operator[](key_type &&k)
			{
				return try_emplace(std::move(k)).first->second;
			}

			template <typename K = key_type>
			mapped_type &at(const key_arg<K> &key)
			{
				auto it = this->find(key);
				if (it == this->end())
					base_internal::ThrowStdOutOfRange("phmap::btree_map::at");
				return it->second;
			}
			template <typename K = key_type>
			const mapped_type &at(const key_arg<K> &key) const
			{
				auto it = this->find(key);
				if (it == this->end())
					base_internal::ThrowStdOutOfRange("phmap::btree_map::at");
				return it->second;
			}
		};

// A common base class for btree_multiset and btree_multimap.
		template <typename Tree>
		class btree_multiset_container : public btree_container<Tree> {
			using super_type = btree_container<Tree>;
			using params_type = typename Tree::params_type;
			using init_type = typename params_type::init_type;
			using is_key_compare_to = typename params_type::is_key_compare_to;

			template <class K>
			using key_arg = typename super_type::template key_arg<K>;

		public:
			using key_type = typename Tree::key_type;
			using value_type = typename Tree::value_type;
			using size_type = typename Tree::size_type;
			using key_compare = typename Tree::key_compare;
			using allocator_type = typename Tree::allocator_type;
			using iterator = typename Tree::iterator;
			using const_iterator = typename Tree::const_iterator;
			using node_type = typename super_type::node_type;

			// Inherit constructors.
			using super_type::super_type;
			btree_multiset_container() {}

			// Range constructor.
			template <class InputIterator>
			btree_multiset_container(InputIterator b, InputIterator e,
			                         const key_compare &comp = key_compare(),
			                         const allocator_type &alloc = allocator_type())
				: super_type(comp, alloc)
			{
				insert(b, e);
			}

			// Initializer list constructor.
			btree_multiset_container(std::initializer_list<init_type> init,
			                         const key_compare &comp = key_compare(),
			                         const allocator_type &alloc = allocator_type())
				: btree_multiset_container(init.begin(), init.end(), comp, alloc) {}

			// Lookup routines.
			template <typename K = key_type>
			size_type count(const key_arg<K> &key) const
			{
				return this->tree_.count_multi(key);
			}

			// Insertion routines.
			iterator insert(const value_type &x)
			{
				return this->tree_.insert_multi(x);
			}
			iterator insert(value_type &&x)
			{
				return this->tree_.insert_multi(std::move(x));
			}
			iterator insert(const_iterator hint, const value_type &x)
			{
				return this->tree_.insert_hint_multi(iterator(hint), x);
			}
			iterator insert(const_iterator hint, value_type &&x)
			{
				return this->tree_.insert_hint_multi(iterator(hint), std::move(x));
			}
			template <typename InputIterator>
			void insert(InputIterator b, InputIterator e)
			{
				this->tree_.insert_iterator_multi(b, e);
			}
			void insert(std::initializer_list<init_type> init)
			{
				this->tree_.insert_iterator_multi(init.begin(), init.end());
			}
			template <typename... Args>
			iterator emplace(Args &&... args)
			{
				return this->tree_.insert_multi(init_type(std::forward<Args>(args)...));
			}
			template <typename... Args>
			iterator emplace_hint(const_iterator hint, Args &&... args)
			{
				return this->tree_.insert_hint_multi(
				           iterator(hint), init_type(std::forward<Args>(args)...));
			}
			iterator insert(node_type &&node)
			{
				if (!node) return this->end();
				iterator res =
				    this->tree_.insert_multi(params_type::key(CommonAccess::GetSlot(node)),
				                             CommonAccess::GetSlot(node));
				CommonAccess::Destroy(&node);
				return res;
			}
			iterator insert(const_iterator hint, node_type &&node)
			{
				if (!node) return this->end();
				iterator res = this->tree_.insert_hint_multi(
				                   iterator(hint),
				                   std::move(params_type::element(CommonAccess::GetSlot(node))));
				CommonAccess::Destroy(&node);
				return res;
			}

			// Deletion routines.
			template <typename K = key_type>
			size_type erase(const key_arg<K> &key)
			{
				return this->tree_.erase_multi(key);
			}
			using super_type::erase;

			// Node extraction routines.
			template <typename K = key_type>
			node_type extract(const key_arg<K> &key)
			{
				auto it = this->find(key);
				return it == this->end() ? node_type() : extract(it);
			}
			using super_type::extract;

			// Merge routines.
			// Moves all elements from `src` into `this`.
			template <
			    typename T,
			    typename phmap::enable_if_t<
			        phmap::conjunction<
			            std::is_same<value_type, typename T::value_type>,
			            std::is_same<allocator_type, typename T::allocator_type>,
			            std::is_same<typename params_type::is_map_container,
			                         typename T::params_type::is_map_container>>::value,
			        int> = 0>
			void merge(btree_container<T> &src)    // NOLINT
			{
				insert(std::make_move_iterator(src.begin()),
				       std::make_move_iterator(src.end()));
				src.clear();
			}

			template <
			    typename T,
			    typename phmap::enable_if_t<
			        phmap::conjunction<
			            std::is_same<value_type, typename T::value_type>,
			            std::is_same<allocator_type, typename T::allocator_type>,
			            std::is_same<typename params_type::is_map_container,
			                         typename T::params_type::is_map_container>>::value,
			        int> = 0>
			void merge(btree_container<T> &&src)
			{
				merge(src);
			}
		};

// A base class for btree_multimap.
		template <typename Tree>
		class btree_multimap_container : public btree_multiset_container<Tree> {
			using super_type = btree_multiset_container<Tree>;
			using params_type = typename Tree::params_type;

		public:
			using mapped_type = typename params_type::mapped_type;

			// Inherit constructors.
			using super_type::super_type;
			btree_multimap_container() {}
		};

	}  // namespace priv



// ----------------------------------------------------------------------
//  btree_set - default values in phmap_fwd_decl.h
// ----------------------------------------------------------------------
	template <typename Key, typename Compare, typename Alloc>
	class btree_set : public priv::btree_set_container<
		priv::btree<priv::set_params<
		Key, Compare, Alloc, /*TargetNodeSize=*/ 256, /*Multi=*/ false>>> {
		using Base = typename btree_set::btree_set_container;

	public:
		btree_set() {}
		using Base::Base;
		using Base::begin;
		using Base::cbegin;
		using Base::end;
		using Base::cend;
		using Base::empty;
		using Base::max_size;
		using Base::size;
		using Base::clear;
		using Base::erase;
		using Base::insert;
		using Base::emplace;
		using Base::emplace_hint;
		using Base::extract;
		using Base::merge;
		using Base::swap;
		using Base::contains;
		using Base::count;
		using Base::equal_range;
		using Base::lower_bound;
		using Base::upper_bound;
		using Base::find;
		using Base::get_allocator;
		using Base::key_comp;
		using Base::value_comp;
	};

// Swaps the contents of two `phmap::btree_set` containers.
// -------------------------------------------------------
	template <typename K, typename C, typename A>
	void swap(btree_set<K, C, A> &x, btree_set<K, C, A> &y)
	{
		return x.swap(y);
	}

// Erases all elements that satisfy the predicate pred from the container.
// ----------------------------------------------------------------------
	template <typename K, typename C, typename A, typename Pred>
	void erase_if(btree_set<K, C, A> &set, Pred pred)
	{
		for (auto it = set.begin(); it != set.end();) {
			if (pred(*it)) {
				it = set.erase(it);
			}
			else {
				++it;
			}
		}
	}

// ----------------------------------------------------------------------
//  btree_multiset - default values in phmap_fwd_decl.h
// ----------------------------------------------------------------------
	template <typename Key, typename Compare,  typename Alloc>
	class btree_multiset : public priv::btree_multiset_container<
		priv::btree<priv::set_params<
		Key, Compare, Alloc, /*TargetNodeSize=*/ 256, /*Multi=*/ true>>> {
		using Base = typename btree_multiset::btree_multiset_container;

	public:
		btree_multiset() {}
		using Base::Base;
		using Base::begin;
		using Base::cbegin;
		using Base::end;
		using Base::cend;
		using Base::empty;
		using Base::max_size;
		using Base::size;
		using Base::clear;
		using Base::erase;
		using Base::insert;
		using Base::emplace;
		using Base::emplace_hint;
		using Base::extract;
		using Base::merge;
		using Base::swap;
		using Base::contains;
		using Base::count;
		using Base::equal_range;
		using Base::lower_bound;
		using Base::upper_bound;
		using Base::find;
		using Base::get_allocator;
		using Base::key_comp;
		using Base::value_comp;
	};

// Swaps the contents of two `phmap::btree_multiset` containers.
// ------------------------------------------------------------
	template <typename K, typename C, typename A>
	void swap(btree_multiset<K, C, A> &x, btree_multiset<K, C, A> &y)
	{
		return x.swap(y);
	}

// Erases all elements that satisfy the predicate pred from the container.
// ----------------------------------------------------------------------
	template <typename K, typename C, typename A, typename Pred>
	void erase_if(btree_multiset<K, C, A> &set, Pred pred)
	{
		for (auto it = set.begin(); it != set.end();) {
			if (pred(*it)) {
				it = set.erase(it);
			}
			else {
				++it;
			}
		}
	}


// ----------------------------------------------------------------------
//  btree_map - default values in phmap_fwd_decl.h
// ----------------------------------------------------------------------
	template <typename Key, typename Value, typename Compare,  typename Alloc>
	class btree_map : public priv::btree_map_container<
		priv::btree<priv::map_params<
		Key, Value, Compare, Alloc, /*TargetNodeSize=*/ 256, /*Multi=*/ false>>> {
		using Base = typename btree_map::btree_map_container;

	public:
		btree_map() {}
		using Base::Base;
		using Base::begin;
		using Base::cbegin;
		using Base::end;
		using Base::cend;
		using Base::empty;
		using Base::max_size;
		using Base::size;
		using Base::clear;
		using Base::erase;
		using Base::insert;
		using Base::emplace;
		using Base::emplace_hint;
		using Base::try_emplace;
		using Base::extract;
		using Base::merge;
		using Base::swap;
		using Base::at;
		using Base::contains;
		using Base::count;
		using Base::equal_range;
		using Base::lower_bound;
		using Base::upper_bound;
		using Base::find;
		using Base::operator[];
		using Base::get_allocator;
		using Base::key_comp;
		using Base::value_comp;
	};

// Swaps the contents of two `phmap::btree_map` containers.
// -------------------------------------------------------
	template <typename K, typename V, typename C, typename A>
	void swap(btree_map<K, V, C, A> &x, btree_map<K, V, C, A> &y)
	{
		return x.swap(y);
	}

// ----------------------------------------------------------------------
	template <typename K, typename V, typename C, typename A, typename Pred>
	void erase_if(btree_map<K, V, C, A> &map, Pred pred)
	{
		for (auto it = map.begin(); it != map.end();) {
			if (pred(*it)) {
				it = map.erase(it);
			}
			else {
				++it;
			}
		}
	}

// ----------------------------------------------------------------------
//  btree_multimap - default values in phmap_fwd_decl.h
// ----------------------------------------------------------------------
	template <typename Key, typename Value, typename Compare, typename Alloc>
	class btree_multimap : public priv::btree_multimap_container<
		priv::btree<priv::map_params<
		Key, Value, Compare, Alloc, /*TargetNodeSize=*/ 256, /*Multi=*/ true>>> {
		using Base = typename btree_multimap::btree_multimap_container;

	public:
		btree_multimap() {}
		using Base::Base;
		using Base::begin;
		using Base::cbegin;
		using Base::end;
		using Base::cend;
		using Base::empty;
		using Base::max_size;
		using Base::size;
		using Base::clear;
		using Base::erase;
		using Base::insert;
		using Base::emplace;
		using Base::emplace_hint;
		using Base::extract;
		using Base::merge;
		using Base::swap;
		using Base::contains;
		using Base::count;
		using Base::equal_range;
		using Base::lower_bound;
		using Base::upper_bound;
		using Base::find;
		using Base::get_allocator;
		using Base::key_comp;
		using Base::value_comp;
	};

// Swaps the contents of two `phmap::btree_multimap` containers.
// ------------------------------------------------------------
	template <typename K, typename V, typename C, typename A>
	void swap(btree_multimap<K, V, C, A> &x, btree_multimap<K, V, C, A> &y)
	{
		return x.swap(y);
	}

// Erases all elements that satisfy the predicate pred from the container.
// ----------------------------------------------------------------------
	template <typename K, typename V, typename C, typename A, typename Pred>
	void erase_if(btree_multimap<K, V, C, A> &map, Pred pred)
	{
		for (auto it = map.begin(); it != map.end();) {
			if (pred(*it)) {
				it = map.erase(it);
			}
			else {
				++it;
			}
		}
	}


}  // namespace btree

#ifdef _MSC_VER
#pragma warning(pop)
#endif


#endif  // PHMAP_BTREE_BTREE_CONTAINER_H_
